On maximal subgroups of infinite index in branch and weakly branch groups
Group Theory
2020-04-06 v1
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.
Keywords
Cite
@article{arxiv.2004.01696,
title = {On maximal subgroups of infinite index in branch and weakly branch groups},
author = {Dominik Francoeur},
journal= {arXiv preprint arXiv:2004.01696},
year = {2020}
}
Comments
27 pages