Maximal subgroups of groups of intermediate growth
Alejandra Garrido (Heinrich Heine Universität Düsseldorf)
Wednesday 20th September, 2017 16:00-17:00 Maths 311B
Studying the maximal subgroups of a group is a basic way of getting an insight into their structure. In the case where the group is countably infinite, one of the first questions one can ask is whether there are any maximal subgroups of infinite index.
The study of maximal subgroups of countably infinite groups has so far mainly concerned classes of groups which are either "small" or "big" in the sense that they are either virtually nilpotent (and so all maximal subgroups are of finite index) or of exponential word growth (and in this case there are uncountably many maximal subgroups of infinite index).
It is natural to investigate this question for groups of intermediate word growth, for instance, some self-similar groups of automorphisms of rooted trees.
I will report on some joint work with Dominik Francoeur where we show that some such groups of intermediate word growth have exactly countably many maximal subgroups of infinite index.