London Algebra Colloquium abstract

Subgroups of finite index and the just infinite property

Colin D. Reid (Queen Mary), 8th October 2009

Abstract

An infinite residually finite (profinite) group G is just infinite if every non-trivial (closed) normal subgroup is of finite index, and hereditarily just infinite if every subgroup of finite index is just infinite. But which subgroups of finite index need to be just infinite to ensure that all of them are? I will present a partial answer to this question, after a brief overview of the basic types of just infinite groups and why they are of interest.