# RCWA

Residue-Class-Wise Affine Groups

Version 4.6.4
Released 2019-03-24

This project is maintained by Stefan Kohl

# RCWA – [R]esidue-[C]lass-[W]ise [A]ffine groups

## A GAP 4 Package

### Version 4.6.4

Author and Maintainer: Stefan Kohl, stefan@mcs.st-and.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 >=4.9.0 in 64-bit mode, ResClasses >=4.7.0, 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.