anu-pq - The anupq command line interface
anu-pq [-b] [-G] [-g] [-i] [-k] [-v] [-s <n>]
[-w <file>] [-c] [-d]
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.
-
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.
-
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.
The anu-pq guide
/usr/share/gap/pkg/anupq/standalone-doc/guide.pdf