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arXiv · 1707.07654

Torsion homology and cellular approximation

Ramón Flores·Fernando Muro
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Abstract

In this note 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 $H_2G$ allows to approximate many groups by colimits of copies of finite $p$-groups. Our examples include interesting families of non-commutative infinite groups, including Burnside groups, certain solvable examples and the first Grigorchuk group. We also provide a counterexample for a conjecture of E. Farjoun.

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Ramón Flores, Fernando Muro. 2017-07-24. Torsion homology and cellular approximation. https://doi.org/10.2140/agt.2019.19.457

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