HOMOLOGY OF FREE ABELIANIZED EXTENSIONS OF GROUPS

Abstract

Let G be a group given by a free presentation G = F/N, and N' the commutator subgroup of N. The quotient F/N' is called a free abelianized extension of G. We study the homology of F/N' with trivial coefficients. In particular, for torsion-free G our main result yields a complete description of the odd torsion in the integral homology of F/N' in terms of the mod p homology of G.