The RCWA Package ================ Abstract This package for GAP 4 introduces a new class of groups which are accessible to computational methods. In principle, it can deal at least with the follo- wing types of groups: - Finite groups. - Free groups of finite rank. - Free products of finitely many finite groups, thus in particular the modular group PSL(2,Z). - Direct products of such groups. - Wreath products of such 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 clas- ses of the integers and which all the above groups embed into. Requirements The RCWA package needs at least GAP 4.4.7, ResClasses 2.5.1, GRAPE 4.0, Poly- cyclic 2.1 and GAPDoc 1.0. All required packages are already present in a standard GAP installation. RCWA can be used under UNIX, under Windows and on the MacIntosh. It is completely written in the GAP language and does neither contain nor require external binaries. In particular, warnings concerning missing binaries issued by GRAPE or other packages can savely be ignored. Installation Like any other GAP package, RCWA must be installed in the pkg/ subdirectory of the GAP distribution. This is accomplished by extracting the distribution file in this directory. When you have done this you can load the package as usual via LoadPackage( "rcwa" );. For further advice on questions of technical nature please see the chap- ter `Auxiliary functions' in the manual. --- If you have problems with this package, wish to make comments or suggestions, or if you find bugs, please send e-mail to Stefan Kohl, kohl@mathematik.uni-stuttgart.de