Abstract

When groups may be built up as graphs of ‘simpler’ groups, it is often of interest to study how good residual finiteness properties of simpler groups can imply residual properties of the whole. The essential case of this theory is the study of residual properties of finite groups. In this talk I will discuss the question of when a graph of finite p-groups is residually p-finite, for p a prime. I will describe the previous theorems in this area for one-edge and finite graphs of groups, and their method of proof. I will then state my recent generalisation of these theorems to potentially infinite graphs of groups, together with an alternative and more natural method of proof. Finally I will briefly describe a usage of these results in the study of accessibility—namely the existence of a finitely generated inaccessible group which is residually p-finite.