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Maximal subgroups of groups of intermediate growth Garrido, Alejandra


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 where the Tits Alternative holds (every subgroup is either virtually soluble or contains a free subgroup) and in the case where there are maximal subgroups of infinite index, there are uncountably many. It is natural to investigate this question for groups of intermediate growth, for instance, some groups of automorphisms of rooted trees. I will report on some recent joint work with Dominik Francoeur where we show that some groups of intermediate growth have exactly countably many maximal subgroups of infinite index.

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