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.