## Algebraic & Geometric Topology

### Torsion homology and cellular approximation

#### 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 $H 2 G$ 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.

#### Article information

Source
Algebr. Geom. Topol., Volume 19, Number 1 (2019), 457-476.

Dates
Revised: 3 September 2018
Accepted: 11 September 2018
First available in Project Euclid: 12 February 2019

https://projecteuclid.org/euclid.agt/1549940438

Digital Object Identifier
doi:10.2140/agt.2019.19.457

Mathematical Reviews number (MathSciNet)
MR3910586

Zentralblatt MATH identifier
07053579

Keywords
Torsion homology cellular group

#### Citation

Flores, Ramón; Muro, Fernando. Torsion homology and cellular approximation. Algebr. Geom. Topol. 19 (2019), no. 1, 457--476. doi:10.2140/agt.2019.19.457. https://projecteuclid.org/euclid.agt/1549940438

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