Wednesday, January 11, 2017 - 14:15 in V4-119
Primitive groups of intermediate word growth
A talk in the 'Oberseminar Gruppen und Geometrie'
||Studying the primitive actions of a group corresponds to studying its maximal subgroups. In the case where the group is countably infinite, one of the first questions one can ask is whether there are any primitive actions on infinite sets; that 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 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. In particular, we show that they are primitive groups of intermediate word growth.
Within the CRC this talk is associated to the project(s): B1, C12, C13