[Up]

AutPGrp manual
Moreover, the pgroup generation method of Newman (1977) and O'Brien
+Moreover, the pgroup generation method of Newman (1977) and O'Brien
(1990) can be modified to compute the automorphism group of a finite
pgroup as outlined in O'Brien (1995). This algorithm is implemented
+pgroup as outlined in O'Brien (1995). This algorithm is implemented
in the ANU pq
C program.
Here we introduce a new function to compute the automorphism group of
a finite pgroup. The underlying algorithm is a refinement of the
+a finite pgroup. The underlying algorithm is a refinement of the
methods described in O'Brien (1995). In particular, this implementation
is more efficient in both time and space requirements and hence has a
wider range of applications than the ANU pq
method. Our package is
@@ 38,7 +38,7 @@ permutation group functions.
The GAP 4 package ANUPQ, which is an interface to most of
the functionality of the ANU pq
C program, uses the AutPGrp package
to compute automorphism groups of pgroups.
+to compute automorphism groups of pgroups.
We have compared our method to the others available in GAP. Our package usually outperforms all but the method designed @@ 46,12 +46,8 @@ for finite abelian groups. We note that small groups library in certain cases and hence our algorithm is more effective if the small groups library is installed.
A GAP 3 version of the methods implemented in this package is available via http://wwwpublic.tubs.de:8080/~beick/so.html 

AutPGrp manual
The AutPGrp package installs a method for AutomorphismGroup
for a
finite pgroup (see also Section Groups of Automorphisms
+finite pgroup (see also Section Groups of Automorphisms
in the GAP Reference Manual).
AutomorphismGroup(
G ) M
The input is a finite pgroup G. If the filters IsPGroup
,
+The input is a finite pgroup G. If the filters IsPGroup
,
IsFinite
and CanEasilyComputePcgs
are set and true for G,
the method selection of GAP 4 invokes this algorithm.
InfoAutGrp V
This is a GAP InfoClass (these are described in Chapter Info Functions in the GAP Reference Manual). By assigning an infolevel +This is a GAP InfoClass (these are described in Chapter Info Functions in the GAP Reference Manual). By assigning an infolevel in the range 1 to 4 via
SetInfoLevel(InfoAutGrp,
infolevel)
@@ 32,9 +32,7 @@ varying levels of information on the pro
the computation, will be obtained.
gap> RequirePackage("autpgrp"); #I  The AutPGrp package  #I  Computing automorphism groups of pgroups  +gap> LoadPackage("autpgrp", false); true gap> G := SmallGroup( 32, 15 ); @@ 50,7 +48,7 @@ gap> AutomorphismGroup(G); <group of size 64 with 6 generators>
The algorithm proceeds by induction down the lower pcentral +The algorithm proceeds by induction down the lower pcentral series of G and the information corresponds to the steps of this induction. In the following example we observe that the method also accepts permutation groups as input, provided @@ 66,14 +64,13 @@ gap> CanEasilyComputePcgs(G); true gap> IsFinite(G); true gap> AutomorphismGroup(G); +gap> A := AutomorphismGroup(G); #I step 1: 2^2  init automorphisms #I step 2: 2^1  aut grp has size 2 #I step 3: 2^1  aut grp has size 8 #I step 4: 2^1  aut grp has size 32 #I final step: convert <group of size 128 with 7 generators> gap> A := last;; gap> A.1; Pcgs([ ( 2,16)( 3,15)( 4,14)( 5,13)( 6,12)( 7,11)( 8,10), ( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11,12,13,14,15,16), @@ 92,5 +89,5 @@ gap> Order(A.1);
[Up] [Previous] [Next] [Index]

AutPGrp manualAutomorphismGroupPGroup(
G [,
flag] ) F
The input is a finite pgroup as above and an optional flag
+The input is a finite pgroup as above and an optional flag
which can be true or false. Here the filters for G need not be
set, but they should be true for G. The possible values for flag
are considered later in Chapter Influencing the algorithm. If
@@ 53,9 +53,7 @@ the output of AutomorphismGroupPGr
ConvertHybridAutGroup(
A ) F
gap> RequirePackage("autpgrp");
#I  The AutPGrp package 
#I  Computing automorphism groups of pgroups 
+gap> LoadPackage("autpgrp", false);
true
gap> H := SmallGroup (729, 34);
@@ 95,12 +93,12 @@ gap> ConvertHybridAutGroup( A );
<group of size 52488 with 11 generators>
Let A be the automorphism group of a pgroup G as computed by
+Let A be the automorphism group of a pgroup G as computed by
AutomorphismGroupPGroup
. Then the following function can compute
a pc group isomorphic to the solvable part of A stored in the record
component A.agGroup. This solvable part forms a subgroup of the
automorphism group which contains at least the automorphisms centralizing
the Frattini factor of G. The pc group facilitates various further
+the Frattini factor of G. The pc group facilitates various further
computations with A.
@@ 122,5 +120,5 @@ Group([ f5, f4^2*f8, f6^2*f9^2, f11^2, f
[Up] [Previous] [Next] [Index]

AutPGrp manual
Februar 2010
+AutPGrp manual
July 2018
\ No newline at end of file
diff pruN 1.81/htm/CHAP004.htm 1.101/htm/CHAP004.htm
 1.81/htm/CHAP004.htm 20160319 22:17:53.000000000 +0000
+++ 1.101/htm/CHAP004.htm 20180909 16:26:36.000000000 +0000
@@ 36,17 +36,17 @@ choices the later sections of this chapt
4.1 Outline of the algorithm
The basic algorithm proceeds by induction
down the lower pcentral series of a given pgroup G; that is, it
successively computes Aut(G_{i}) for the quotients G_{i} = G / P_{i}(G) of
the descending sequence of subgroups defined by P_{1}(G) = G and
P_{i+1}(G)=[P_{i}(G),G] P_{i}(G)^{p} for igeq1. Hence, in the initial
step of the algorithm, Aut(G_{2}) = GL(d,p) where d is the rank of
the elementary abelian group G_{2}. In the inductive step it determines
Aut(G_{i+1}) from Aut(G_{i}). For this purpose we introduce
an action of Aut(G_{i}) on a certain elementary abelian pgroup M
(the pmultiplicator of G_{i}). The main computation of the inductive
step is the determination of the stabiliser in Aut(G_{i}) of a subgroup
U of M (the allowable subgroup for G_{i+1}). This stabiliser
+down the lower pcentral series of a given pgroup G; that is, it
+successively computes Aut(G_{i}) for the quotients G_{i} = G / P_{i}(G) of
+the descending sequence of subgroups defined by P_{1}(G) = G and
+P_{i+1}(G)=[P_{i}(G),G] P_{i}(G)^{p} for i ≥ 1. Hence, in the initial
+step of the algorithm, Aut(G_{2}) = GL(d,p) where d is the rank of
+the elementary abelian group G_{2}. In the inductive step it determines
+Aut(G_{i+1}) from Aut(G_{i}). For this purpose we introduce
+an action of Aut(G_{i}) on a certain elementary abelian pgroup M
+(the pmultiplicator of G_{i}). The main computation of the inductive
+step is the determination of the stabiliser in Aut(G_{i}) of a subgroup
+U of M (the allowable subgroup for G_{i+1}). This stabiliser
calculation is the bottleneck of the algorithm.
Our package incorporates a number of refinements designed to simplify
@@ 54,35 +54,35 @@ this stabiliser computation. Some of the
and hence they are not always invoked. The features outlined below
allow the user to select them.
Observe that the initial step of the algorithm returns GL(d,p). But
Aut(G) may induce on G_{2} a proper subgroup, say K, of GL(d,p).
Any intermediate subgroup of GL(d,p) which contains K suffices for
+Observe that the initial step of the algorithm returns GL(d,p). But
+Aut(G) may induce on G_{2} a proper subgroup, say K, of GL(d,p).
+Any intermediate subgroup of GL(d,p) which contains K suffices for
the algorithm and we supply two methods to construct a suitable subgroup:
these use characteristic subgroups or invariants of normal subgroups of G.
+these use characteristic subgroups or invariants of normal subgroups of G.
(See Section The initialisation step.)
In the inductive step an action of Aut(G_{i}) on an elementary abelian
group M is used. This action is computed as a matrix action on a vector
space. To simplify the orbitstabiliser computation of the subspace U
of M, we can construct the stabiliser of U by iteration over a sequence
of Aut(G_{i})invariant subspaces of M.
+In the inductive step an action of Aut(G_{i}) on an elementary abelian
+group M is used. This action is computed as a matrix action on a vector
+space. To simplify the orbitstabiliser computation of the subspace U
+of M, we can construct the stabiliser of U by iteration over a sequence
+of Aut(G_{i})invariant subspaces of M.
(See Section Stabilisers in matrix groups.)
Orbitstabiliser computations in finite solvable groups given by a
polycyclic generating sequence are much more efficient than generic
computations of this type. Thus our algorithm makes use of a large
solvable normal subgroup S of Aut(G_{i}). Further, it is useful if
the generating set of Aut(G_{i}) outside S is as small as possible.
To achieve this we determine a permutation representation of Aut(G_{i})/S
+solvable normal subgroup S of Aut(G_{i}). Further, it is useful if
+the generating set of Aut(G_{i}) outside S is as small as possible.
+To achieve this we determine a permutation representation of Aut(G_{i})/S
and use this to reduce the number of generators if possible. (See Section
Searching for a small generating set.)
4.2 The initialisation step
Assume we seek to compute the automorphism group of a pgroup G
having Frattini rank d. We first determine as small as possible a
subgroup of GL(d, p) whose extension can act on G.
+Assume we seek to compute the automorphism group of a pgroup G
+having Frattini rank d. We first determine as small as possible a
+subgroup of GL(d, p) whose extension can act on G.
The user can choose the initialisation routine by assigning
InitAutGroup
to any one of the following.
@@ 93,15 +93,15 @@ The user can choose the initialisation r
InitAutomorphismGroupChar
to use the characteristic subgroups;

InitAutomorphismGroupFull
to use the full GL(d,p).
+ InitAutomorphismGroupFull
to use the full GL(d,p).
a) Minimal Overgroups
We determine the minimal overgroups of the Frattini subgroup of
G and compute invariants of these which must be respected by the
automorphism group of G. We partition the minimal overgroups and
compute the stabiliser in GL(d, p) of this partition.
+G and compute invariants of these which must be respected by the
+automorphism group of G. We partition the minimal overgroups and
+compute the stabiliser in GL(d, p) of this partition.
The partition of the minimal overgroups is computed using the
function PGFingerprint( G, U )
. This is the timeconsuming
@@ 110,10 +110,10 @@ overwrite the function PGFingerpri
b) Characteristic Subgroups
Compute a generating set for the stabiliser in GL (d, p) of
a chain of characteristic subgroups of G. In practice, we construct
+Compute a generating set for the stabiliser in GL (d, p) of
+a chain of characteristic subgroups of G. In practice, we construct
a characteristic chain by determining 2step centralisers and omega
subgroups of factors of the lower pcentral series.
+subgroups of factors of the lower pcentral series.
However, there are often other characteristic subgroups which are not
found by these approaches. The user can overwrite the function
@@ 122,34 +122,33 @@ found by these approaches. The user can
c) Defaults
In the method for AutomorphismGroup
we use a default strategy:
if the value fracp^{d}1p1 is less than 1000, then we
+if the value [(p^{d}−1)/(p−1)] is less than 1000, then we
use the minimal overgroup approach, otherwise the characteristic
subgroups are employed. An exception is made for homogeneous abelian
groups where we initialise the algorithm with the full group GL(d,p).
+groups where we initialise the algorithm with the full group GL(d,p).
4.3 Stabilisers in matrix groups
Consider the ith inductive step of the algorithm. Here A leq
Aut(G_{i}) acts as matrix group on the elementary abelian pgroup
M and we want to determine the stabiliser of a subgroup U leqM.

We use the MeatAxe to compute a series of Ainvariant subspaces
through M such that each factor in the series is irreducible as
Amodule. Then we use this series to break the computation
of Stab_{A}(U) into several smaller orbitstabiliser calculations.

Note that a theoretic argument yields an Ainvariant subspace
of M a priori: the nucleus N. This is always used to split
the computation up. However, it may happen that N = M and hence
+Consider the ith inductive step of the algorithm. Here A ≤ Aut(G_{i}) acts as matrix group on the elementary abelian pgroup
+M and we want to determine the stabiliser of a subgroup U ≤ M.
+
+We use the MeatAxe to compute a series of Ainvariant subspaces
+through M such that each factor in the series is irreducible as
+Amodule. Then we use this series to break the computation
+of Stab_{A}(U) into several smaller orbitstabiliser calculations.
+
+Note that a theoretic argument yields an Ainvariant subspace
+of M a priori: the nucleus N. This is always used to split
+the computation up. However, it may happen that N = M and hence
results in no improvement.
CHOP_MULT V
The invariant series through M is computed and used if the
+The invariant series through M is computed and used if the
global variable CHOP_MULT
is set to true
. Otherwise, the algorithm
tries to determine Stab_{A}(U) in one step. By default, CHOP_MULT
+tries to determine Stab_{A}(U) in one step. By default, CHOP_MULT
is true
.
@@ 160,17 +159,17 @@ set for the automorphism group of the cu
If the automorphism group is soluble, we store a polycyclic generating
set; otherwise, we store such a generating set for a large soluble
normal subgroup S of the automorphism group A, and as few generators
outside as possible. If S = A and a polycyclic generating set for
S is known, many steps of the algorithm proceed more rapidly.
+normal subgroup S of the automorphism group A, and as few generators
+outside as possible. If S = A and a polycyclic generating set for
+S is known, many steps of the algorithm proceed more rapidly.
NICE_STAB V
It may be both timeconsuming and difficult to reduce the number of
generators for A outside S. Note that if the initialisation of the
+generators for A outside S. Note that if the initialisation of the
algorithm is by InitAutomorphismGroupOver
, then we always know a
permutation representation for A/S. Occasionally the search for
+permutation representation for A/S. Occasionally the search for
a small generating set is expensive. If this is observed, one
could set the flag NICE_STAB
to false
and the algorithm no
longer invokes this search.
@@ 179,7 +178,7 @@ longer invokes this search.
4.5 An interactive version of the algorithm
The choice of initialisation and the choice of chopping of the
pmultiplicator can also be driven by an interactive version
+pmultiplicator can also be driven by an interactive version
of the algorithm. We give an example.
@@ 250,7 +249,7 @@ Two points are worthy of comment.
First, the interactive version of the algorithm permits the user to
make a suitable choice in each step of the algorithm instead of making
one choice at the beginning. Secondly, the output of the Info
function
shows the ranks of the pmultiplicator and allowable subgroup,
+shows the ranks of the pmultiplicator and allowable subgroup,
and thus allow the user to observe the scale of difficulty
of the computation.
@@ 264,5 +263,5 @@ the Up] [Previous] [Next] [Index]

AutPGrp manual
Februar 2010
+AutPGrp manual
July 2018
\ No newline at end of file
diff pruN 1.81/htm/CHAP005.htm 1.101/htm/CHAP005.htm
 1.81/htm/CHAP005.htm 20160319 22:17:53.000000000 +0000
+++ 1.101/htm/CHAP005.htm 20180909 16:26:36.000000000 +0000
@@ 4,36 +4,36 @@
5 Additional Features of the Package
As an additional feature of this package we provide some functions to
count extensions of pgroups and Lie algebras over GF(p). These
functions have been used in counting the 2groups of size 2^{10}.
+count extensions of pgroups and Lie algebras over GF(p). These
+functions have been used in counting the 2groups of size 2^{10}.
NumberOfPClass2PGroups( n, p, k )
determines the number of ngenerator pgroups of pclass 2 with
Frattini subgroup of order 2^{k}.
+determines the number of ngenerator pgroups of pclass 2 with
+Frattini subgroup of order 2^{k}.
NumberOfPClass2PGroups( n, p )
returns a list of of numbers of ngenerator pgroups of pclass 2
with Frattini subgroup of order 2^{k} for k in 1, ..., n(n+1)/2.
+returns a list of of numbers of ngenerator pgroups of pclass 2
+with Frattini subgroup of order 2^{k} for k in 1, …, n(n+1)/2.
NumberOfClass2LieAlgebras( n, p, k )
determines the number of ngenerator Lie algebras of class 2 over
GF(p) with derived Lie subalgebra of dimension k.
+determines the number of ngenerator Lie algebras of class 2 over
+GF(p) with derived Lie subalgebra of dimension k.
NumberOfClass2LieAlgbras( n, p )
returns a list of of numbers of ngenerator Lie algebras of class 2
over GF(p) with derived Lie subalgebra of dimension k for k in
1, ..., n(n1)/2.
+returns a list of of numbers of ngenerator Lie algebras of class 2
+over GF(p) with derived Lie subalgebra of dimension k for k in
+1, …, n(n−1)/2.

AutPGrp manual
Februar 2010
+AutPGrp manual
July 2018
\ No newline at end of file
diff pruN 1.81/htm/chapters.htm 1.101/htm/chapters.htm
 1.81/htm/chapters.htm 20160319 22:17:53.000000000 +0000
+++ 1.101/htm/chapters.htm 20180909 16:26:36.000000000 +0000
@@ 16,5 +16,5 @@
Index

AutPGrp manual
Februar 2010
+AutPGrp manual
July 2018
\ No newline at end of file
diff pruN 1.81/htm/indxA.htm 1.101/htm/indxA.htm
 1.81/htm/indxA.htm 20160319 22:17:53.000000000 +0000
+++ 1.101/htm/indxA.htm 19700101 00:00:00.000000000 +0000
@@ 1,23 +0,0 @@
AutPGrp : a GAP 4 package  Index A

AutPGrp : a GAP 4 package  Index A
Acknowledgements 4.6
 Additional Features of the Package 5.0
 An interactive version of the algorithm 4.5
 AutomorphismGroup 2.0
 AutomorphismGroupPGroup 3.0

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Februar 2010

\ No newline at end of file
diff pruN 1.81/htm/indxC.htm 1.101/htm/indxC.htm
 1.81/htm/indxC.htm 20160319 22:17:53.000000000 +0000
+++ 1.101/htm/indxC.htm 19700101 00:00:00.000000000 +0000
@@ 1,20 +0,0 @@
AutPGrp : a GAP 4 package  Index C

AutPGrp : a GAP 4 package  Index C
 CHOP_MULT 4.3.1
 ConvertHybridAutGroup 3.0

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Februar 2010

\ No newline at end of file
diff pruN 1.81/htm/indxI.htm 1.101/htm/indxI.htm
 1.81/htm/indxI.htm 20160319 22:17:53.000000000 +0000
+++ 1.101/htm/indxI.htm 19700101 00:00:00.000000000 +0000
@@ 1,21 +0,0 @@
AutPGrp : a GAP 4 package  Index I

AutPGrp : a GAP 4 package  Index I
 Influencing the algorithm 4.0
 InfoAutGrp 2.0
 Introduction 1.0

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Februar 2010

\ No newline at end of file
diff pruN 1.81/htm/indxN.htm 1.101/htm/indxN.htm
 1.81/htm/indxN.htm 20160319 22:17:53.000000000 +0000
+++ 1.101/htm/indxN.htm 19700101 00:00:00.000000000 +0000
@@ 1,22 +0,0 @@
AutPGrp : a GAP 4 package  Index N

AutPGrp : a GAP 4 package  Index N
 NICE_STAB 4.4.1
 NumberOfClass2LieAlgbras 5.0
 NumberOfClass2LieAlgebras 5.0
 NumberOfPClass2PGroups 5.0 5.0

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Februar 2010

\ No newline at end of file
diff pruN 1.81/htm/indxO.htm 1.101/htm/indxO.htm
 1.81/htm/indxO.htm 20160319 22:17:53.000000000 +0000
+++ 1.101/htm/indxO.htm 19700101 00:00:00.000000000 +0000
@@ 1,19 +0,0 @@
AutPGrp : a GAP 4 package  Index O

AutPGrp : a GAP 4 package  Index O
 Outline of the algorithm 4.1

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Februar 2010

\ No newline at end of file
diff pruN 1.81/htm/indxP.htm 1.101/htm/indxP.htm
 1.81/htm/indxP.htm 20160319 22:17:53.000000000 +0000
+++ 1.101/htm/indxP.htm 19700101 00:00:00.000000000 +0000
@@ 1,19 +0,0 @@
AutPGrp : a GAP 4 package  Index P

AutPGrp : a GAP 4 package  Index P
 PcGroupAutPGroup 3.0

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Februar 2010

\ No newline at end of file
diff pruN 1.81/htm/indxS.htm 1.101/htm/indxS.htm
 1.81/htm/indxS.htm 20160319 22:17:53.000000000 +0000
+++ 1.101/htm/indxS.htm 19700101 00:00:00.000000000 +0000
@@ 1,21 +0,0 @@
AutPGrp : a GAP 4 package  Index S

AutPGrp : a GAP 4 package  Index S
 Searching for a small generating set 4.4
 SetInfoLevel 2.0
 Stabilisers in matrix groups 4.3

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Februar 2010

\ No newline at end of file
diff pruN 1.81/htm/indxT.htm 1.101/htm/indxT.htm
 1.81/htm/indxT.htm 20160319 22:17:53.000000000 +0000
+++ 1.101/htm/indxT.htm 19700101 00:00:00.000000000 +0000
@@ 1,21 +0,0 @@
AutPGrp : a GAP 4 package  Index T

AutPGrp : a GAP 4 package  Index T
 The automorphism group method 2.0
 The initialisation step 4.2
 The underlying function 3.0

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Februar 2010

\ No newline at end of file
diff pruN 1.81/htm/theindex.htm 1.101/htm/theindex.htm
 1.81/htm/theindex.htm 20160319 22:17:53.000000000 +0000
+++ 1.101/htm/theindex.htm 20180909 16:26:36.000000000 +0000
@@ 1,18 +1,62 @@
AutPGrp : a GAP 4 package  Index _
+AutPGrp : a GAP 4 package  Index
AutPGrp : a GAP 4 package  Index _
+AutPGrp : a GAP 4 package  Index
_
A
C
I
N
O
P
S
T
+A
+C
+I
+N
+O
+P
+S
+T
+
A
+
+ Acknowledgements 4.6
+
 Additional Features of the Package 5.0
+
 An interactive version of the algorithm 4.5
+
 AutomorphismGroup 2.0
+
 AutomorphismGroupPGroup 3.0
+
+
C
+
+
I
+
+
N
+
+ NICE_STAB 4.4.1
+
 NumberOfClass2LieAlgbras 5.0
+
 NumberOfClass2LieAlgebras 5.0
+
 NumberOfPClass2PGroups 5.0 5.0
+
+
O
+
+ Outline of the algorithm 4.1
+
+
P
+
+ PcGroupAutPGroup 3.0
+
+
S
+
+
T
+
[Up]

AutPGrp manual
Februar 2010
+AutPGrp manual
July 2018
\ No newline at end of file
diff pruN 1.81/LICENSE 1.101/LICENSE
 1.81/LICENSE 19700101 00:00:00.000000000 +0000
+++ 1.101/LICENSE 20180909 16:26:36.000000000 +0000
@@ 0,0 +1,351 @@
+The AutPGrp package is free software; you can redistribute and/or modify
+it under the terms of the GNU General Public License as published by
+the Free Software Foundation; either version 2 of the License, or (at
+your opinion) any later version.
+
+The AutPGrp package is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+General Public License for more details.
+
+Version 2 of the GNU General Public License follows.
+
+ GNU GENERAL PUBLIC LICENSE
+ Version 2, June 1991
+
+ Copyright (C) 1989, 1991 Free Software Foundation, Inc.,
+ 51 Franklin Street, Fifth Floor, Boston, MA 021101301 USA
+ Everyone is permitted to copy and distribute verbatim copies
+ of this license document, but changing it is not allowed.
+
+ Preamble
+
+ The licenses for most software are designed to take away your
+freedom to share and change it. By contrast, the GNU General Public
+License is intended to guarantee your freedom to share and change free
+softwareto make sure the software is free for all its users. This
+General Public License applies to most of the Free Software
+Foundation's software and to any other program whose authors commit to
+using it. (Some other Free Software Foundation software is covered by
+the GNU Lesser General Public License instead.) You can apply it to
+your programs, too.
+
+ When we speak of free software, we are referring to freedom, not
+price. Our General Public Licenses are designed to make sure that you
+have the freedom to distribute copies of free software (and charge for
+this service if you wish), that you receive source code or can get it
+if you want it, that you can change the software or use pieces of it
+in new free programs; and that you know you can do these things.
+
+ To protect your rights, we need to make restrictions that forbid
+anyone to deny you these rights or to ask you to surrender the rights.
+These restrictions translate to certain responsibilities for you if you
+distribute copies of the software, or if you modify it.
+
+ For example, if you distribute copies of such a program, whether
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+
+ We protect your rights with two steps: (1) copyright the software, and
+(2) offer you this license which gives you legal permission to copy,
+distribute and/or modify the software.
+
+ Also, for each author's protection and ours, we want to make certain
+that everyone understands that there is no warranty for this free
+software. If the software is modified by someone else and passed on, we
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+ Finally, any free program is threatened constantly by software
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+ The precise terms and conditions for copying, distribution and
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+
+ GNU GENERAL PUBLIC LICENSE
+ TERMS AND CONDITIONS FOR COPYING, DISTRIBUTION AND MODIFICATION
+
+ 0. This License applies to any program or other work which contains
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+
+ How to Apply These Terms to Your New Programs
+
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+possible use to the public, the best way to achieve this is to make it
+free software which everyone can redistribute and change under these terms.
+
+ To do so, attach the following notices to the program. It is safest
+to attach them to the start of each source file to most effectively
+convey the exclusion of warranty; and each file should have at least
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+ Copyright (C)
+
+ This program is free software; you can redistribute it and/or modify
+ it under the terms of the GNU General Public License as published by
+ the Free Software Foundation; either version 2 of the License, or
+ (at your option) any later version.
+
+ This program is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+ GNU General Public License for more details.
+
+ You should have received a copy of the GNU General Public License along
+ with this program; if not, write to the Free Software Foundation, Inc.,
+ 51 Franklin Street, Fifth Floor, Boston, MA 021101301 USA.
+
+Also add information on how to contact you by electronic and paper mail.
+
+If the program is interactive, make it output a short notice like this
+when it starts in an interactive mode:
+
+ Gnomovision version 69, Copyright (C) year name of author
+ Gnomovision comes with ABSOLUTELY NO WARRANTY; for details type `show w'.
+ This is free software, and you are welcome to redistribute it
+ under certain conditions; type `show c' for details.
+
+The hypothetical commands `show w' and `show c' should show the appropriate
+parts of the General Public License. Of course, the commands you use may
+be called something other than `show w' and `show c'; they could even be
+mouseclicks or menu itemswhatever suits your program.
+
+You should also get your employer (if you work as a programmer) or your
+school, if any, to sign a "copyright disclaimer" for the program, if
+necessary. Here is a sample; alter the names:
+
+ Yoyodyne, Inc., hereby disclaims all copyright interest in the program
+ `Gnomovision' (which makes passes at compilers) written by James Hacker.
+
+ , 1 April 1989
+ Ty Coon, President of Vice
+
+This General Public License does not permit incorporating your program into
+proprietary programs. If your program is a subroutine library, you may
+consider it more useful to permit linking proprietary applications with the
+library. If this is what you want to do, use the GNU Lesser General
+Public License instead of this License.
diff pruN 1.81/PackageInfo.g 1.101/PackageInfo.g
 1.81/PackageInfo.g 20170330 12:06:18.000000000 +0000
+++ 1.101/PackageInfo.g 20180909 16:26:36.000000000 +0000
@@ 7,8 +7,8 @@ SetPackageInfo( rec(
PackageName := "AutPGrp",
Subtitle := "Computing the Automorphism Group of a pGroup",
Version := "1.8",
Date := "25/11/2016",
+Version := "1.10",
+Date := "30/07/2018",
Persons := [
rec(
@@ 29,6 +29,24 @@ Persons := [
Institution := "TU Braunschweig"),
rec(
+ LastName := "Horn",
+ FirstNames := "Max",
+ IsAuthor := false,
+ IsMaintainer := true,
+ Email := "max.horn@math.unigiessen.de",
+ WWWHome := "http://www.quendi.de/math",
+ PostalAddress := Concatenation(
+ "AG Algebra\n",
+ "Mathematisches Institut\n",
+ "JustusLiebigUniversität Gießen\n",
+ "Arndtstraße 2\n",
+ "35392 Gießen\n",
+ "Germany" ),
+ Place := "Gießen",
+ Institution := "JustusLiebigUniversität Gießen"
+ ),
+
+ rec(
LastName := "O'Brien",
FirstNames := "Eamonn",
IsAuthor := true,
@@ 41,23 +59,25 @@ Persons := [
"Private Bag 92019\n Auckland\n New Zealand\n" ),
Place := "Auckland",
Institution := "University of Auckland"
 )
+ ),
],
Status := "accepted",
CommunicatedBy := "Derek F. Holt (Warwick)",
AcceptDate := "09/2000",
PackageWWWHome := "http://www.icm.tubs.de/~beick/so.html",

+PackageWWWHome := "https://gappackages.github.io/autpgrp/",
+README_URL := Concatenation( ~.PackageWWWHome, "README" ),
+PackageInfoURL := Concatenation( ~.PackageWWWHome, "PackageInfo.g" ),
+SourceRepository := rec(
+ Type := "git",
+ URL := "https://github.com/gappackages/autpgrp",
+),
+IssueTrackerURL := Concatenation( ~.SourceRepository.URL, "/issues" ),
+ArchiveURL := Concatenation( ~.SourceRepository.URL,
+ "/releases/download/v", ~.Version,
+ "/autpgrp", ~.Version ),
ArchiveFormats := ".tar.gz",
ArchiveURL := Concatenation(
 "http://www.icm.tubs.de/~beick/soft/autpgrp/autpgrp", ~.Version ),
README_URL := "http://www.icm.tubs.de/~beick/soft/autpgrp/README",
PackageInfoURL := "http://www.icm.tubs.de/~beick/soft/autpgrp/PackageInfo.g",
# ArchiveURL := Concatenation( ~.PackageWWWHome, "autpgrp", ~.Version ),
# README_URL := Concatenation( ~.PackageWWWHome, "README" ),
# PackageInfoURL := Concatenation( ~.PackageWWWHome, "PackageInfo.g" ),
AbstractHTML :=
"The AutPGrp package introduces a new function to compute the automorphism group of a finite $p$group. The underlying algorithm is a refinement of the methods described in O'Brien (1995). In particular, this implementation is more efficient in both time and space requirements and hence has a wider range of applications than the ANUPQ method. Our package is written in GAP code and it makes use of a number of methods from the GAP library such as the MeatAxe for matrix groups and permutation group functions. We have compared our method to the others available in GAP. Our package usually outperforms all but the method designed for finite abelian groups. We note that our method uses the small groups library in certain cases and hence our algorithm is more effective if the small groups library is installed.",
@@ 72,13 +92,15 @@ PackageDoc := rec(
Autoload := true),
Dependencies := rec(
 GAP := ">=4.4",
+ GAP := ">=4.7",
NeededOtherPackages := [],
SuggestedOtherPackages := [],
ExternalConditions := [] ),
AvailabilityTest := ReturnTrue,
Autoload := true,
+
+TestFile := "tst/testall.g",
+
Keywords := ["pgroup", "automorphism group"]
));
diff pruN 1.81/tst/manual.example2.tst 1.101/tst/manual.example2.tst
 1.81/tst/manual.example2.tst 19700101 00:00:00.000000000 +0000
+++ 1.101/tst/manual.example2.tst 20180909 16:26:36.000000000 +0000
@@ 0,0 +1,44 @@
+gap> START_TEST("");
+
+#
+gap> SetInfoLevel( InfoAutGrp, 1 );
+
+#
+gap> G := SmallGroup( 32, 15 );
+
+gap> AutomorphismGroup(G);
+#I step 1: 2^2  init automorphisms
+#I step 2: 2^2  aut grp has size 2
+#I step 3: 2^1  aut grp has size 32
+#I final step: convert
+
+gap> G := DihedralGroup( IsPermGroup, 2^5 );
+Group([ (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16), (2,16)(3,15)(4,14)(5,13)
+(6,12)(7,11)(8,10) ])
+gap> IsPGroup(G);
+true
+gap> CanEasilyComputePcgs(G);
+true
+gap> IsFinite(G);
+true
+gap> A := AutomorphismGroup(G);
+#I step 1: 2^2  init automorphisms
+#I step 2: 2^1  aut grp has size 2
+#I step 3: 2^1  aut grp has size 8
+#I step 4: 2^1  aut grp has size 32
+#I final step: convert
+
+gap> A.1;
+Pcgs([ (2,16)(3,15)(4,14)(5,13)(6,12)(7,11)(8,10),
+ (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16), (1,3,5,7,9,11,13,15)(2,4,6,8,10,
+ 12,14,16), (1,5,9,13)(2,6,10,14)(3,7,11,15)(4,8,12,16),
+ (1,9)(2,10)(3,11)(4,12)(5,13)(6,14)(7,15)(8,16) ]) >
+[ (1,2)(3,16)(4,15)(5,14)(6,13)(7,12)(8,11)(9,10),
+ (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16), (1,3,5,7,9,11,13,15)(2,4,6,8,10,
+ 12,14,16), (1,5,9,13)(2,6,10,14)(3,7,11,15)(4,8,12,16),
+ (1,9)(2,10)(3,11)(4,12)(5,13)(6,14)(7,15)(8,16) ]
+gap> Order(A.1);
+16
+
+#
+gap> STOP_TEST( "" ,1);
diff pruN 1.81/tst/manual.example3.tst 1.101/tst/manual.example3.tst
 1.81/tst/manual.example3.tst 19700101 00:00:00.000000000 +0000
+++ 1.101/tst/manual.example3.tst 20180909 16:26:36.000000000 +0000
@@ 0,0 +1,49 @@
+gap> START_TEST("");
+
+#
+gap> SetInfoLevel( InfoAutGrp, 1 );
+
+#
+gap> H := SmallGroup (729, 34);
+
+gap> A := AutomorphismGroupPGroup(H);
+#I step 1: 3^2  init automorphisms
+#I step 2: 3^1  aut grp has size 8
+#I step 3: 3^2  aut grp has size 72
+#I step 4: 3^1  aut grp has size 5832
+#I final step: convert
+rec(
+ agAutos :=
+ [ Pcgs([ f1, f2, f3, f4, f5, f6 ]) > [ f2, f1, f3^2, f5^2, f4^2, f6^2 ],
+ Pcgs([ f1, f2, f3, f4, f5, f6 ]) > [ f1, f2^2, f3^2*f5, f4^2*f6, f5,
+ f6 ], Pcgs([ f1, f2, f3, f4, f5, f6 ]) >
+ [ f1^2, f2^2, f3*f4^2*f5^2*f6, f4^2*f6, f5^2*f6, f6 ],
+ Pcgs([ f1, f2, f3, f4, f5, f6 ]) > [ f1*f3, f2, f3*f5^2, f4*f6^2, f5,
+ f6 ], Pcgs([ f1, f2, f3, f4, f5, f6 ]) >
+ [ f1, f2*f3, f3*f4, f4, f5*f6, f6 ],
+ Pcgs([ f1, f2, f3, f4, f5, f6 ]) > [ f1*f4, f2, f3*f6^2, f4, f5, f6 ],
+ Pcgs([ f1, f2, f3, f4, f5, f6 ]) > [ f1, f2*f4, f3, f4, f5, f6 ],
+ Pcgs([ f1, f2, f3, f4, f5, f6 ]) > [ f1*f5, f2, f3, f4, f5, f6 ],
+ Pcgs([ f1, f2, f3, f4, f5, f6 ]) > [ f1, f2*f5, f3*f6, f4, f5, f6 ],
+ Pcgs([ f1, f2, f3, f4, f5, f6 ]) > [ f1*f6, f2, f3, f4, f5, f6 ],
+ Pcgs([ f1, f2, f3, f4, f5, f6 ]) > [ f1, f2*f6, f3, f4, f5, f6 ] ],
+ agOrder := [ 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3 ], glAutos := [ ],
+ glOper := [ ], glOrder := 1, group := , one := IdentityMapping( ), size := 52488 )
+gap> ConvertHybridAutGroup( A );
+
+gap> H := SmallGroup (729, 34);;
+gap> A := AutomorphismGroupPGroup(H);;
+#I step 1: 3^2  init automorphisms
+#I step 2: 3^1  aut grp has size 8
+#I step 3: 3^2  aut grp has size 72
+#I step 4: 3^1  aut grp has size 5832
+#I final step: convert
+gap> B := PcGroupAutPGroup( A );
+
+gap> I := InnerAutGroupPGroup( B );
+Group([ f5, f4^2*f8, f6^2*f9^2, f11^2, f10^2, of ... ])
+
+#
+gap> STOP_TEST( "" ,1);
diff pruN 1.81/tst/testall.g 1.101/tst/testall.g
 1.81/tst/testall.g 19700101 00:00:00.000000000 +0000
+++ 1.101/tst/testall.g 20180909 16:26:36.000000000 +0000
@@ 0,0 +1,3 @@
+LoadPackage("autpgrp");
+TestDirectory(DirectoriesPackageLibrary("autpgrp", "tst"), rec(exitGAP := true));
+FORCE_QUIT_GAP(1);