ANUPQ

A GAP 4 package providing
an interface to the ANU pq C program
of Eamonn O'Brien

Authors:
Eamonn O'Brien,
Werner Nickel,
Greg Gamble
Language: GAP 4 and C
Operating System: UNIX
Current version: 1.4 (1278 KB) [Requires at least GAP 4.3fix4]
Previous version: 1.1 (1147 KB) [Works with GAP 4.2 to GAP 4.3fix3]
README file: README.anupq (12 KB)
Package home page: http://www.math.rwth-aachen.de/~Greg.Gamble/ANUPQ/

Description

The ANUPQ package provides an interactive interface to the ANU pq C program. Versions 1.1+ supersede the previous GAP 3 version (1.0) in many ways. In particular, they provide an interactive interface using the IOStream technology introduced in GAP 4.2.

Version 1.1 will work with any version of GAP in the range 4.2 to 4.3fix3, but will not work with any later version of GAP. If possible it is recommended to update to the latest version of GAP.

Version 1.4 of the package requires GAP 4.3 with bugfix 4 applied, and version 1.1 of the AutPGrp package. There have been various improvements in efficiency made between versions 1.1 and 1.4. However, you will need version 1.1 if you have not upgraded your GAP to version 4.3fix4 (or better).

Versions 1.1+ of the ANUPQ package provide an interface to the following algorithms implemented by the ANU pq C program:

1. A p-quotient algorithm to compute a power-commutator presentation for a p-group. The algorithm implemented here is based on that described in Newman and O'Brien (1996), Havas and Newman (1980), and papers referred to there. The current implementation incorporates the following features:
   1. collection from the left (see Vaughan-Lee, 1990); Vaughan-Lee's implementation of this collection algorithm is used in the program;
   2. an improved consistency algorithm (see Vaughan-Lee, 1984);
   3. new exponent law enforcement and power routines;
   4. closing of relations under the action of automorphisms;
   5. some formula evaluation.
2. A p-group generation algorithm to generate descriptions of p-groups. The algorithm implemented here is based on the algorithms described in Newman (1977) and O'Brien (1990).
3. A standard presentation algorithm used to compute a canonical power-commutator presentation of a p-group. The algorithm implemented here is described in O'Brien (1994).

4. an algorithm which can be used to compute the automorphism group of a p-group. The algorithm implemented is described in O'Brien (1994).

   However, this part of the pq C program is not accessible from ANUPQ 1.1+. Instead, users are advised to consider the GAP 4 package AutPGrp by Bettina Eick and Eamonn O'Brien, which implements a better algorithm in GAP for the computation of automorphism groups of p-groups. Where necessary ANUPQ 1.1+ accesses the AutPGrp package to compute automorphism groups of p-groups.

ANUPQ manuals

• HTML package manual: Table of Contents, Index.
• DVI package manual: package manual (261 KB) package manual (377 KB)
• PDF standalone manual: guide (190 KB)

Authors' addresses

Eamonn O'Brien

Department of Mathematics
University of Auckland
Auckland, Private Bag 92019
New Zealand

email: obrien@math.auckland.ac.nz

Werner Nickel
Fachbereich 4, AG 2
Technische Universität Darmstadt
Schlossgartenstr. 7
64289 Darmstadt
Germany

email: nickel@mathematik.tu-darmstadt.de

Greg Gamble
Centre for Discrete Mathematics and Computing, Department of Information Technology and Electrical Engineering
The University of Queensland
Brisbane, Queensland, 4072
AUSTRALIA

email: gregg@itee.uq.edu.au

References

[HN80] George Havas and M. F. Newman, Application of computers to questions like those of Burnside, Burnside groups (Bielefeld, 1977) Lecture Notes in Math. 806, pp. 211-230. Springer-Verlag, 1980.

[NB96] M. F. Newman and E. A. O'Brien (1996), Application of computers to questions like those of Burnside II, Internat. J. Algebra Comput. 6, 593-605, (1996).

[New77] M. F. Newman, Determination of groups of prime-power order, Group theory (Canberra, 1975), Lecture Notes in Math. 573, pp. 73-84, Springer-Verlag, 1977.

[OBr90] E. A. O'Brien, The p-group generation algorithm, J. Symbolic Comput., 9, 677-698, (1990).

[OBr94] E. A. O'Brien, Isomorphism testing for p-groups, J. Symbolic Comput., 17, 133-147, (1994).

[OBr95] E. A. O'Brien, Computing automorphism groups of p-groups, Computational Algebra and Number Theory, (Sydney, 1992) pp. 83-90. Kluwer Academic Publishers, Dordrecht, 1995.

[VL84] M. R. Vaughan-Lee, An Aspect of the Nilpotent Quotient Algorithm, Computational Group Theory (Durham, 1982), pp. 75-84. Academic Press, 1984.

[VL90a] Michael R. Vaughan-Lee, Collection from the left, J. Symbolic Comput., 9, 725-733, (1990).

[VL90b] Michael R. Vaughan-Lee, The restricted Burnside problem, London Mathematical Society Monographs (New Ser.) #5, Clarendon Press, New York, Oxford, 1990.