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 $H_2(G;{\mathbb{F}}_p)$. The context of the problem, which is related to a conjecture of Quillen, is presented, as well as example calculations.

12 pages, 1 figure, 2 tables