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

                                                  November 2024                                        ANU-PQ(1)