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Torsion homology and cellular approximation

Ramón Flores and Fernando Muro

Algebraic & Geometric Topology 19 (2019) 457–476
Abstract

We describe the role of the Schur multiplier in the structure of the p–torsion of discrete groups. More concretely, we show how the knowledge of H2G allows us to approximate many groups by colimits of copies of p–groups. Our examples include interesting families of noncommutative infinite groups, including Burnside groups, certain solvable groups and branch groups. We also provide a counterexample for a conjecture of Emmanuel Farjoun.

Keywords
Torsion, homology, cellular, group
Mathematical Subject Classification 2010
Primary: 20F99, 55P60
References
Publication
Received: 27 March 2018
Revised: 3 September 2018
Accepted: 11 September 2018
Published: 6 February 2019
Authors
Ramón Flores
Departamento de Matemáticas
Facultad de Ciencias
Universidad Autónoma de Madrid
Madrid
Spain
Fernando Muro
Facultad de Matemáticas
Departamento de Álgebra
Universidad de Sevilla
Sevilla
Spain