ANU-PQ(1)

🦋 ANU-PQ(1) · General Commands Manual 🦋

okay bestie, this is the manual page for anu-pq 🎀 It's the command line interface for the ANU pq program, and it's giving main character energy ✨

✨ 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, so go check that out if you want the full tea ☕

Okay so, the ANU p-Quotient Program (pq) is named for the p-quotient algorithm it was the first to implement 🍓 but now it's lowkey a whole buffet. Via menus, it gives you access to implementations of all of these algorithms:

1. A p-quotient algorithm to compute a power-commutator presentation for a p-group. The algorithm implemented here is based on the one described in Newman and O’Brien (1996), Havas and Newman (1980), and the papers referred to there. Another description of the algorithm appears in Vaughan-Lee (1990b). A FORTRAN implementation of this algorithm was programmed by Alford & Havas, and its basic data structures are retained. The current implementation incorporates the following features:
   • a. collection from the left (see Vaughan-Lee, 1990b); Vaughan-Lee’s implementation 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 of 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 — lets you input a group presentation using a “basic\ format. See ??. 🌈
• -G — this one's for GAP 4 users 🫶 It's basically the same as setting -g -i -k all at once, except it uses GAP’s iostream to send requests to GAP so it can compute stabilisers when it needs to.
• -g — if groups are generated using p-group generation, their presentations get written to a file in a GAP compatible format. You can pick the file name with -w, and the default is GAP library. -iThis provides access to the Standard Presentation Menu, which you can use to build the standard presentation of a given p-group.
• -k — the presentation can be defined and supplied using certain key words. Examples of this format live in the 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 happen in an integer array, y. The space of this array is 1000000 by default, but you can set it to n. See the discussion on strategies to minimise time and space later in this document. ⭐
• -v — gives you the version of the ANU p-Quotient program and then exits. 🍓
• -w <file> — group descriptions get written in GAP format to <file>. You have to use -g alongside this one 💅 If the program is compiled using the RUN TIME option, there are two extra runtime options:
• -c — the maximum exponent-p class to be considered. 💖
• -d — a bound on the number of defining generator 🦋
• -n <k> — forces the first k generators to be left or right Engel element, but only if -l or -r (or both) is also present. Otherwise it gets ignored. 🫧

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💌 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. Iconic credits, no notes 🙌

🗺️ SEE ALSO 🗺️

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

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Okay bestie, that's the whole page 🫶 It's dated November 2025 and filed under ANU-PQ(1), so now you're officially cleared to use it 💖🌈