Brauer-Fowler Bounds for Elements of Odd Prime Order

[2608.15194] Brauer-Fowler Bounds for Elements of Odd Prime Order Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Group Theory arXiv:2608.15194 (math) [Submitted on 15 Aug 2026] Title: Brauer-Fowler Bounds for Elements of Odd Prime Order Authors: Alessandro Dioguardi Burgio , Kıvanç Ersoy , Edoardo Salati View a PDF of the paper titled Brauer-Fowler Bounds for Elements of Odd Prime Order, by Alessandro Dioguardi Burgio and 2 other authors View PDF HTML (experimental) Abstract: The Brauer--Fowler theorem bounds the order of a finite simple group in terms of the order of the centralizer of an involution. Hartley proved an automorphism version, bounding the order of a finite simple group in terms of the order of an automorphism and the order of its fixed-point subgroup. Strunkov asked whether, in the involution case, the order of the centralizer can be replaced by the number of involutions commuting with the given involution; this was recently answered affirmatively by Skresanov. Motivated by this question, and in contrast with Hartley's use of the order of a fixed-point subgroup, we study what can be deduced from counting elements of prescribed prime order inside such a subgroup. We show that the direct analogue of Skresanov's result fails for elements of odd prime order. We prove that if \(G\) is a finite simple group, \(x\in G\) has odd prime order \(p\), \(C_G(x)\) contains at most \(k\) elements of order \(p\), and the exponent of \(C_G(x)\) is at most \(e\), then \(|G|\) is bounded in terms of \(k\) and \(e\). Subjects: Group Theory (math.GR) Cite as: arXiv:2608.15194 [math.GR] (or arXiv:2608.15194v1 [math.GR] for this version) https://doi.org/10.48550/arXiv.2608.15194 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Kıvanç Ersoy PD. Dr. [ view email ] [v1] Sat, 15 Aug 2026 12:22:44 UTC (14 KB) Full-text links: Access Paper: View a PDF of the paper titled Brauer-Fowler Bounds for Elements of Odd Prime Order, by Alessandro Dioguardi Burgio and 2 other authors View PDF HTML (experimental) TeX Source view license Current browse context: math.GR < prev | next > new | recent | 2026-08 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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