# Projective resolutions for graph products

Research paper by Daniel E. Cohen

Indexed on: 15 Oct '93Published on: 15 Oct '93Published in: Mathematics - Group Theory

#### Abstract

Let $\Gamma$ be a finite graph together with a group $G_v$ at each vertex $v$. The graph product $G(\Gamma)$ is obtained from the free product of all $G_v$ by factoring out by the normal subgroup generated by $\{g^{-1}h^{-1}gh; g\in G_v, h\in G_w\}$ for all adjacent $v,w$. In this note we construct a projective resolution for $G(\Gamma)$ given projective resolutions for each $G_v$, and obtain some applications.