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The AutPGrp package
-------------------
AutPGrp is a GAP 4 package for computing automorphism groups of p-groups.
Given an arbitrary finite group, the computation of its automorphism
group is a very difficult task. Pioneer work in this area was carried out
by Felsch & Neubueser (1970), whose algorithm used the output of their
subgroup lattice program. A technique developed by Neubueser in the early
1970s sought to compute the automorphism group viewed as a permutation
group acting on unions of certain conjugacy classes of the group. A
similar method was implemented by Hulpke (1997) in the GAP 4 library.
Recently, Cannon & Holt (1999) presented a new algorithm which uses a
``hybrid group'' approach.
More efficient approaches are available to determine the automorphism
group for groups satisfying certain properties. Following the work of
Shoda (1928), Hulpke in 1997 implemented a practical method for finite
abelian groups in the GAP 4 library. Wursthorn (1993) adapted modular
group algebra techniques to compute the automorphism groups of p-groups;
the GAP 3 share package Sisyphos includes an implementation. Smith (1994)
introduced an algorithm for finite solvable groups which is available in
the AutAg share package of GAP 3.
Moreover, the p-group generation method of Newman (1977) and O'Brien
(1990) can be modified to compute the automorphism group of a finite
p-group as outlined in O'Brien (1995). This algorithm is implemented in
the ANU pq C program.
In the AutPGrp package we introduce 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 ANU pq 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.
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 p-groups.
We have compared our method to the others available in GAP. Our package
usually out-performs 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.
Note that since version 1.1 of AutPGrp, at least GAP 4.3fix4 is required.
Authors
-------
The AutPGrp package was written by:
Bettina Eick,
Institut Computational Mathematics,
TU Braunschweig,
Pockelsstr. 14, D-38106 Braunschweig, Germany
e-mail: beick@tu-bs.de
Eamonn O'Brien
Department of Mathematics
University of Auckland
Private Bag 92019, Auckland, New Zealand
e-mail: obrien@math.auckland.ac.nz
Installing the AutPGrp package
------------------------------
To install the AutPGrp package, move the archive file 'autpgrp.zoo' or
'autpgrp.tar.gz' into the `pkg' directory in which you plan to install
AutPGrp. Usually, this will be the directory `pkg' in the hierarchy of
your version of GAP 4. (However, it is also possible to keep an additional
`pkg' directory in your private directories, see section "ref:Installing
GAP Packages" of the GAP 4 reference manual for details on how to do this.)
Then unpack the archive file and that's it!
Bug reports
-----------
If you encounter problems, please contact Bettina Eick <b.eick@tu-bs.de>.
When sending a bug report, remember we will need to be able to reproduce
the problem; so please include:
* The version of GAP you are using; either look at the header when
you start up GAP, or at the gap> prompt type: VERSION;
* The operating system you are using e.g. Linux, SunOS 5.8 = Solaris
2.8, IRIX 6.5, ...
* A script in GAP that demonstrates the bug, along with a description
of why it's a bug (e.g. by adding comments to the script - recall,
comments in GAP begin with a #).
- Bettina Eick
e-mail: b.eick@tu-bs.de
www: http://www.icm.tu-bs.de/~beick/so.html
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