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Quelle README.md
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[](https://github.com/gap-packages/rcwa/actions/workflows/CI.yml)
[](https://codecov.io/gh/gap-packages/rcwa)
# RCWA -- [R]esidue-[C]lass-[W]ise [A]ffine groups
## A GAP 4 Package
Author and Maintainer: Stefan Kohl, sk239@st-andrews.ac.uk
## Abstract
This package for GAP 4 provides implementations of algorithms and methods for
computing in certain infinite permutation groups acting on the set of
integers. It can be used to investigate the following types of groups and
many more:
- Finite groups.
- Free groups of finite rank.
- Free products of finitely many finite groups.
- Direct products of such groups.
- Wreath products of such groups with finite groups and with (Z,+).
- Subgroups of any such groups.
Among these groups there are finitely generated groups which are not finitely
presented, and such with unsolvable membership problem. Further, any finite
group embeds into some divisible torsion group which RCWA can deal with.
With the help of this package, the author has found a countable simple group
which is generated by involutions interchanging disjoint residue classes of
the integers and which all the above groups embed into.
For details on how to use the RCWA package, see the package documentation in
the `doc` subdirectory -- either view its HTML version (chap0.html) with a
browser, or its PDF version (manual.pdf) with a PDF viewer.
## Requirements
This version of RCWA needs GAP >=4.11.1 in 64-bit mode, ResClasses >=4.7.1,
GRAPE >=4.7, Polycyclic >=2.11, FR >=2.2.1, GAPDoc >=1.5.1 and Utils >=0.40.
All required packages are already present in a standard GAP installation.
RCWA can be used on all platforms for which GAP is available. It is
completely written in the GAP language and does neither contain nor require
external binaries.
## Installation
Like any other GAP package, RCWA is usually installed in the pkg/
subdirectory of the GAP distribution. This is accomplished by extracting the
package archive file in this directory. After this you can load the package
as usual via
LoadPackage( "rcwa" );
For further advice on questions of technical nature please see the chapter
`Installation and Auxiliary Functions` in the RCWA manual.
## Distribution and Updates
New releases of this package are put online on the package web pages
- https://gap-packages.github.io/rcwa/
- https://www.gap-system.org/Packages/rcwa.html
and distributed with GAP.
---
If you use RCWA in some of your work, then please let me know. -- I am
interested very much in any applications of this package. Also please
let me know if you have problems with this package, or if you find a bug.
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2026-03-28
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