Generators for Group Homology and a Vanishing Conjecture

Abstract

Letting G = F/R be a finitely-presented group, Hopf's formula expresses the second integral homology of G in terms of F and R. Expanding on previous work, we explain how to find generators of H 2 (G; F p ). The context of the problem, which is related to a conjecture of Quillen, is presented, as well as example calculations.