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)