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Maximal subgroups of a family of iterated monodromy groups

Part of: Structure and classification of infinite or finite groups

Published online by Cambridge University Press:  17 April 2024

Karthika Rajeev  and
Anitha Thillaisundaram
Karthika Rajeev
Affiliation:
Fakultät für Mathematik, Universität Bielefeld, Bielefeld, Germany, Email: krajeev@math.uni-bielefeld.de
Anitha Thillaisundaram*
Affiliation:
Centre for Mathematical Sciences, Lund University, Lund, Sweden
*
Corresponding author: Anitha Thillaisundaram; Email: anitha.thillaisundaram@math.lu.se
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Abstract

The Basilica group is a well-known 2-generated weakly branch, but not branch, group acting on the binary rooted tree. Recently, a more general form of the Basilica group has been investigated by Petschick and Rajeev, which is an $s$-generated weakly branch, but not branch, group that acts on the $m$-adic tree, for $s,m\ge 2$. A larger family of groups, which contains these generalised Basilica groups, is the family of iterated monodromy groups. With the new developments by Francoeur, the study of the existence of maximal subgroups of infinite index has been extended from branch groups to weakly branch groups. Here we show that a subfamily of iterated monodromy groups, which more closely resemble the generalised Basilica groups, have maximal subgroups only of finite index.

Keywords

Groups acting on rooted treesiterated monodromy groupsweakly branch groupsmaximal subgroups

MSC classification

Primary: 20E08: Groups acting on trees
Secondary: 20E28: Maximal subgroups
Type
Research Article
Information
Glasgow Mathematical Journal , First View , pp. 1 - 22
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Glasgow Mathematical Journal Trust

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