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A Mathematica notebook for computing the homology of iterated products of groups. (English) Zbl 1230.20050

Iglesias, Andrés (ed.) et al., Mathematical software – ICMS 2006. Second international congress on mathematical software, Castro Urdiales, Spain, September 1–3, 2006. Proceedings. Berlin: Springer (ISBN 978-3-540-38084-9/pbk). Lecture Notes in Computer Science 4151, 47-57 (2006).
Summary: Let \(G\) be a group which admits the structure of an iterated product of central extensions and semidirect products of Abelian groups \(G_i\) (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 \(G_i\) and the products involved. Computational results provided by our program have allowed the simplification of some of the formulae involved in the calculation of \(H_n(G)\). Consequently the efficiency of the method has been improved as well. We include some executions and examples.
For the entire collection see [Zbl 1195.68008].

MSC:

20J05 Homological methods in group theory
20-04 Software, source code, etc. for problems pertaining to group theory
20E22 Extensions, wreath products, and other compositions of groups
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