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Maximal subgroups of Grigorchuk-Gupta-Sidki (GGS-)groups

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The GGS -groups were some of the early positive answers to the famous Burnside problem. These groups act on infinite rooted trees and are easy to describe, plus possess interesting properties. A natural aspect of these groups to study is their maximal subgroups, and in particular, whether these groups have maximal subgroups of infinite index. It was proved by Pervova in 2005 that the torsion GGS -groups do not have maximal subgroups of infinite index. In this talk, I will consider the remaining non-torsion GGS -groups. This is joint work with Dominik Francoeur.

This talk is part of the Birmingham and Warwick Algebra Seminar series.

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