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GGS-groups acting on trees of growing degrees

Skipper, Rachel and Thillaisundaram, Anitha LU (2026) In Communications in Algebra 54(1). p.365-392
Abstract

We consider analogues of Grigorchuk-Gupta-Sidki (GGS-)groups acting on trees of growing degree; the so-called growing GGS-groups. These groups are not just infinite and do not possess the congruence subgroup property, but many of them are branch and have the p-congruence subgroup property, for a prime p. Among them, we find groups with maximal subgroups only of finite index, and with infinitely many such maximal subgroups. These give the first examples of finitely generated branch groups with infinitely many finite-index maximal subgroups. Additionally, we prove that congruence quotients of growing GGS-groups associated to a defining vector of zero sum give rise to Beauville groups.

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author
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organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Beauville groups, branch groups, congruence subgroup property, Groups acting on irregular rooted trees, maximal subgroups
in
Communications in Algebra
volume
54
issue
1
pages
28 pages
publisher
Taylor & Francis
external identifiers
  • scopus:105010431582
ISSN
0092-7872
DOI
10.1080/00927872.2025.2525388
language
English
LU publication?
yes
additional info
Publisher Copyright: © 2025 The Author(s). Published with license by Taylor & Francis Group, LLC.
id
8bcec5f5-9a97-4e5d-9f0e-511bf7ad2dd4
date added to LUP
2026-01-08 15:48:32
date last changed
2026-01-08 15:49:31
@article{8bcec5f5-9a97-4e5d-9f0e-511bf7ad2dd4,
  abstract     = {{<p>We consider analogues of Grigorchuk-Gupta-Sidki (GGS-)groups acting on trees of growing degree; the so-called growing GGS-groups. These groups are not just infinite and do not possess the congruence subgroup property, but many of them are branch and have the p-congruence subgroup property, for a prime p. Among them, we find groups with maximal subgroups only of finite index, and with infinitely many such maximal subgroups. These give the first examples of finitely generated branch groups with infinitely many finite-index maximal subgroups. Additionally, we prove that congruence quotients of growing GGS-groups associated to a defining vector of zero sum give rise to Beauville groups.</p>}},
  author       = {{Skipper, Rachel and Thillaisundaram, Anitha}},
  issn         = {{0092-7872}},
  keywords     = {{Beauville groups; branch groups; congruence subgroup property; Groups acting on irregular rooted trees; maximal subgroups}},
  language     = {{eng}},
  number       = {{1}},
  pages        = {{365--392}},
  publisher    = {{Taylor & Francis}},
  series       = {{Communications in Algebra}},
  title        = {{GGS-groups acting on trees of growing degrees}},
  url          = {{http://dx.doi.org/10.1080/00927872.2025.2525388}},
  doi          = {{10.1080/00927872.2025.2525388}},
  volume       = {{54}},
  year         = {{2026}},
}