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Maximal subgroups of a family of iterated monodromy groups

Rajeev, Karthika and Thillaisundaram, Anitha LU (2024) In Glasgow Mathematical Journal
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 ≥ 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... (More)

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 ≥ 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.

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type
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publication status
in press
subject
keywords
Groups acting on rooted trees, iterated monodromy groups, maximal subgroups, weakly branch groups
in
Glasgow Mathematical Journal
publisher
Cambridge University Press
external identifiers
  • scopus:85190752811
ISSN
0017-0895
DOI
10.1017/S0017089524000120
language
English
LU publication?
yes
id
e391b8b1-c181-47b6-86c8-02c24d255516
date added to LUP
2024-04-29 09:12:46
date last changed
2024-04-29 09:13:00
@article{e391b8b1-c181-47b6-86c8-02c24d255516,
  abstract     = {{<p>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 ≥ 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.</p>}},
  author       = {{Rajeev, Karthika and Thillaisundaram, Anitha}},
  issn         = {{0017-0895}},
  keywords     = {{Groups acting on rooted trees; iterated monodromy groups; maximal subgroups; weakly branch groups}},
  language     = {{eng}},
  publisher    = {{Cambridge University Press}},
  series       = {{Glasgow Mathematical Journal}},
  title        = {{Maximal subgroups of a family of iterated monodromy groups}},
  url          = {{http://dx.doi.org/10.1017/S0017089524000120}},
  doi          = {{10.1017/S0017089524000120}},
  year         = {{2024}},
}