ANU-PQ(1)

NAME
anu-pq - The anupq command line interface

SYNOPSIS
anu-pq [-b] [-G] [-g] [-i] [-k] [-v] [-s <n>] [-w <file>] [-c] [-d]

DESCRIPTION
This is the man page for the ANU pq program. It briefly documents the parameters. The main documentation is available in the guide.pdf file.

The ANU p-Quotient Program (pq) is named for the p-quotient algorithm that it first implemented. Now, via menus it provides access to implementations of all the following algorithms:

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. Another description of the algorithm appears in Vaughan-Lee (1990b). A FOR- TRAN implementation of this algorithm was programmed by Alford & Havas. The basic data structures of that implementation are retained. The current implementation incorporates the following features: a. collection from the left (see Vaughan-Lee, 1990b); Vaughan-Lee’s implemen- tation of this collection algorithm is used in the program; b. an improved consistency algorithm (see Vaughan-Lee, 1982); c. new exponent law enforcement and power routines; d. closing of relations under the action of automorphisms; e. some formula evaluation.

2.  A p-group generation algorithm to generate descriptions of p-groups.

3.  A standard presentation algorithm used to compute a canonical power-commutator presentation of a p-group.

4.  An algorithm which can be used to compute the automorphism group of a p- group.

OPTIONS
The options -l, -r and -e can be used to enforce Engel conditions on the nilpotent quotient to be calculated. All these options have to be followed by a positive integer <n>. Their meaning is the following:

The program may be invoked with the following runtime parameters:

•   -b: A “basic\ format can be used to input a group presentation. See ??.

•   -G: This option is used by GAP 4. It is essentially equivalent to setting the switches -g -i -k simultaneously, except that it uses GAP’s iostream to direct requests to GAP to compute stabilisers when necessary.

•   -g: If groups are generated using p-group generation, then their presentations are written to a file in a GAP compatible format. The name of the file may be selected using the -w option; the default is GAP library. -iThis provides access to the Standard Presentation Menu, which can be used to construct the standard presentation of a given p-group.

•   -k: The presentation may be defined and supplied using certain key words. Examples of this format can be found in those files in the examples directory whose names commence with keywords . This option cannot be used with -b.

•   -s <n>: All computations of power-commutator presentations occur in an integer array, y – the space of this array, by default 1000000, is set to n. See the discussion on strategies to minimise time and space later in this document.

•   -v: Gives the version of the ANU p-Quotient program and exits.

•   -w <file> Group descriptions are written in GAP format to file. -g must be used in con- junction with this parameter. If the program is compiled using the RUN TIME option, then there are two additional runtime options:

•   -c: The maximum exponent-p class to be considered.

•   -d: A bound on the number of defining generator

•   -n <k>: This option forces the first k generators to be left or right Engel element if also the option -l or -r (or both) is present. Otherwise it is ignored.

COPYRIGHT
The ANU nq program is Copyright (C) by Greg Gamble Greg.Gamble@uwa.edu.au, Werner Nickel, Eamonn O'Brien obrien@math.auckland.ac.nz, Max Horn horn@mathematik.uni-kl.de.

SEE ALSO
The anu-pq guide /usr/share/gap/pkg/anupq/standalone-doc/guide.pdf