A mathematica notebook for computing the homology of iterated products of groups

Abstract

Let G be a group which admits the structure of an iterated product of central extensions and semidirect products of abelian groups d (both finite and infinite). We describe a Mathematica 4-0 notebook for computing the homology of G, in terms of some homological models for the factor groups Gi and the products involved. Computational results provided by our program have allowed the simplification of some of the formulae involved in the calculation of Hn(G). Consequently the efficiency of the method has been improved as well. We include some executions and examples. © Springer-Verlag Berlin Heidelberg 2006.