16:00
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 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.