Version 2.2.1
September 29, 2006
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
RCWA is a package for GAP 4, which provides methods for computing with Residue Class-Wise Affine groups. In principle, this package can deal at least with the following types of groups and their subgroups:
Finite groups, and certain divisible torsion groups which they embed into.
Free groups of finite rank.
Free products of finitely many finite groups, thus in particular the modular group PSL(2,Z).
Direct products of the above groups.
Wreath products of the above groups with finite groups and with (Z,+).
With substancial help of this package, the author has found a countable simple group which is generated by involutions interchanging residue classes of the integers and into which all the above groups embed. This simple group has an uncountable series of simple subgroups, which is parametrized by the sets of odd primes.
(C) 2003 - 2006 by Stefan Kohl. This package is distributed under the GNU General Public License.
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 inviting me to give a talk on the subject in Lausanne in April 2006, and for his hint on how to construct wreath products of residue class-wise affine groups with (Z,+). I would like to thank Otto H. Kegel, Katrin Tent and Oliver Röndigs for their related invitations to Freiburg resp. Bielefeld in February and March 2006.
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