GGS-groups acting on trees of growing degrees

[2405.20961] GGS-groups acting on trees of growing degrees Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Group Theory arXiv:2405.20961 (math) [Submitted on 31 May 2024 ( v1 ), last revised 15 Aug 2026 (this version, v2)] Title: GGS-groups acting on trees of growing degrees Authors: Rachel Skipper , Anitha Thillaisundaram View a PDF of the paper titled GGS-groups acting on trees of growing degrees, by Rachel Skipper and Anitha Thillaisundaram View PDF HTML (experimental) 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. Comments: 28 pages; revised version with an added Section 3.4 on the Hausdorff dimension. This is an Accepted Manuscript of an article published by Taylor & Francis in Communications in Algebra on 10th July 2025, available at: this https URL Subjects: Group Theory (math.GR) Cite as: arXiv:2405.20961 [math.GR] (or arXiv:2405.20961v2 [math.GR] for this version) https://doi.org/10.48550/arXiv.2405.20961 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Anitha Thillaisundaram [ view email ] [v1] Fri, 31 May 2024 16:02:52 UTC (31 KB) [v2] Sat, 15 Aug 2026 09:04:01 UTC (32 KB) Full-text links: Access Paper: View a PDF of the paper titled GGS-groups acting on trees of growing degrees, by Rachel Skipper and Anitha Thillaisundaram View PDF HTML (experimental) TeX Source view license Current browse context: math.GR < prev | next > new | recent | 2024-05 Change to browse by: math References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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