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arXiv · 2004.01696

On maximal subgroups of infinite index in branch and weakly branch groups

Dominik Francoeur
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Abstract

We generalise a technical tool, originally developed by Pervova for the study of maximal subgroups in Grigorchuk and GGS groups, to all weakly branch groups satisfying a natural condition, and in particular to all branch groups. We then use this tool to prove that every maximal subgroup of infinite index of a branch group is also a branch group. As a further application of this result, we show that every maximal subgroup of the Basilica group is of finite index.

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Dominik Francoeur. 2020-04-03. On maximal subgroups of infinite index in branch and weakly branch groups. https://arxiv.org/abs/2004.01696

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