Version 3.1.1
October 18, 2011
Stefan Kohl
Email: stefan@mcs.st-and.ac.uk
Homepage: http://www.gap-system.org/DevelopersPages/StefanKohl/
RCWA is a package for GAP 4. It provides implementations of algorithms and methods for computing in certain infinite permutation groups acting on the set of integers. 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,+).
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 -- see [Koh10].
© 2003 - 2011 by Stefan Kohl.
RCWA is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 2 of the License, or (at your option) any later version.
RCWA is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.
For a copy of the GNU General Public License, see the file GPL in the etc directory of the GAP distribution or see http://www.gnu.org/licenses/gpl.html.
I thank Bettina Eick for communicating this package and for her kind help in improving its documentation. Further I thank the two anonymous referees for their constructive criticism and their helpful suggestions.
Concerning mathematical contributions, I am grateful to John P. McDermott for the discovery that the group discussed in Section 7.1 is isomorphic to the Higman-Thompson group (which is a finitely presented infinite simple group), and to Laurent Bartholdi for his hint on how to construct wreath products of residue-class-wise affine groups with (ℤ,+).
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