# Homological models for semidirect products of finitely generated Abelian groups

@article{lvarez2012HomologicalMF, title={Homological models for semidirect products of finitely generated Abelian groups}, author={V{\'i}ctor {\'A}lvarez and Jos{\'e} Andr{\'e}s Armario and Marialuisa Frau and Pedro Real Jurado}, journal={Applicable Algebra in Engineering, Communication and Computing}, year={2012}, volume={23}, pages={101-127} }

Let G be a semidirect product of finitely generated Abelian groups. We provide a method for constructing an explicit contraction (special homotopy equivalence) from the reduced bar construction of the group ring of G, $${\overline{B}(\mathsf{\textstyle Z\kern-0.4em Z}[G])}$$ , to a much smaller DGA-module hG. Such a contraction is called a homological model for G and is used as the input datum in the methods described in Álvarez et al. (J Symb Comput 44:558–570, 2009; 2012) for calculating a… Expand

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