Amenable quotients of graph products of groups

Abstract

Abstract: A group is amenable if it admits a left-invariant Haar measure (there are many different equivalent definitions). It is well known fact that not all groups are amenable, the easiest example being the free group. One can then ask: if group G is not amenable, can we at least homomorphically map every non-trivial element of G onto a non-trivial element of an amenable group, i.e. does every non-trivial element of G survive in some amenable quotient of G? Groups with this property are called residually amenable. In the talk I will introduce the graph product of groups, group-theoretic construction naturally generalising the concept of direct and free product in the category of groups, and show that the class of residually amenable groups is closed under forming graph products. This talk is based on the paper (http://arxiv.org/abs/1505.05001) co-authored with F. Berlai.