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RCWA

Residue-Class-Wise Affine Groups

Version 2.5.4

September 26, 2007

Stefan Kohl
e-mail: kohl@mathematik.uni-stuttgart.de
WWW: http://www.cip.mathematik.uni-stuttgart.de/~kohlsn/
Address:
Institut für Geometrie und Topologie
Pfaffenwaldring 57
Universität Stuttgart
70550 Stuttgart
Germany

Abstract

RCWA is a package for GAP 4. It provides implementations of algorithms and methods for computing in certain infinite permutation groups. In principle, this package can deal at least with the following types of groups and their subgroups:

With substancial help of this package, the author has found a countable simple group which has an uncountable series of simple subgroups. This simple group is generated by involutions which interchange disjoint residue classes of the integers. All the above groups embed into it.

Copyright

© 2003 - 2007 by Stefan Kohl. This package is distributed under the GNU General Public License.

Acknowledgements

I am very grateful to Bettina Eick for communicating this package and for her kind help in improving its documentation. Further I would like to thank the two anonymous referees for their constructive criticism and their helpful suggestions.

I am also very grateful to Laurent Bartholdi for his hint on how to construct wreath products of residue-class-wise affine groups with (Z,+). Last but not least I would like to thank all the people who have invited me so far to give talks on the subject in their seminars and on their conferences.

Contents

1. About the RCWA Package
2. Residue-Class-Wise Affine Mappings
3. Residue-Class-Wise Affine Groups
4. Residue-Class-Wise Affine Monoids
5. Examples
6. The Algorithms Implemented in RCWA
7. Installation and auxiliary functions
 7.5 Building the manual
  7.5-1 RCWABuildManual
 7.6 Loading and saving bitmap pictures
  7.6-1 SaveAsBitmapPicture
 7.7 Running demonstrations
  7.7-1 RunDemonstration
 7.8 Some general utility functions

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