Cohomology and finite subgroups of small cancellation quotients of free products

Abstract

In this paper we study small cancellation quotients of free products. In particular we calculate their cohomology and, via a theorem of Serre, classify their finite subgroups. The results obtained are the natural analogues of the corresponding results for small cancellation quotients of free groups obtained in Huebschmann [6] (but see also Collins-Huebschmann[3]). They also generalize results of McCool[9] on elements of finite order in quotients of free products and similar conclusions have been obtained by Howie [5] for one-relator quotients of free products of locally indicable groups.