A residually finite analogue of Kegel's theorem on splitting automorphisms

[2604.01011] A residually finite analogue of Kegel's theorem on splitting automorphisms Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Group Theory arXiv:2604.01011 (math) [Submitted on 1 Apr 2026 ( v1 ), last revised 11 Jun 2026 (this version, v2)] Title: A residually finite analogue of Kegel's theorem on splitting automorphisms Authors: Alfonso Di Bartolo , Kıvanç Ersoy , Giovanni Falcone View a PDF of the paper titled A residually finite analogue of Kegel's theorem on splitting automorphisms, by Alfonso Di Bartolo and 2 other authors View PDF HTML (experimental) Abstract: Thompson proved that every finite group admitting a fixed-point-free automorphism of prime order is nilpotent, and Kegel showed that the same conclusion holds for finite groups admitting a splitting automorphism of prime order. Motivated by these results, Sozutov asked whether a \(p'\)-group admitting a splitting automorphism of prime order is locally nilpotent if \[ \langle g, g^\varphi, \dots, g^{\varphi^{p-1}} \rangle \] is nilpotent for every \(g \in G\), \cite[Problem 10.59]{kourovka21}. We prove that if \(G\) is a periodic residually finite group admitting a splitting automorphism of prime order \(p\) then \(G\) is nilpotent of class bounded in terms of \(p\). This gives an affirmative answer, for residually finite groups, to the problem of Sozutov. We also prove that a possible counterexample to Sozutov's problem cannot be a Tarski monster. Subjects: Group Theory (math.GR) MSC classes: 20E36 20F50 20F28 20D45 Cite as: arXiv:2604.01011 [math.GR] (or arXiv:2604.01011v2 [math.GR] for this version) https://doi.org/10.48550/arXiv.2604.01011 Focus to learn more arXiv-issued DOI via DataCite Related DOI : https://doi.org/10.1007/s00013-026-02278-3 Focus to learn more DOI(s) linking to related resources Submission history From: Kıvanç Ersoy PD. Dr. [ view email ] [v1] Wed, 1 Apr 2026 15:16:11 UTC (8 KB) [v2] Thu, 11 Jun 2026 15:13:24 UTC (7 KB) Full-text links: Access Paper: View a PDF of the paper titled A residually finite analogue of Kegel's theorem on splitting automorphisms, by Alfonso Di Bartolo and 2 other authors View PDF HTML (experimental) TeX Source view license Current browse context: math.GR < prev | next > new | recent | 2026-04 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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