Mixed identities for simple locally finite groups

[2608.14537] Mixed identities for simple locally finite groups Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Group Theory arXiv:2608.14537 (math) [Submitted on 14 Aug 2026] Title: Mixed identities for simple locally finite groups Authors: Henry Bradford , Kıvanç Ersoy , Jakob Schneider , Andreas Thom View a PDF of the paper titled Mixed identities for simple locally finite groups, by Henry Bradford and 3 other authors View PDF HTML (experimental) Abstract: A mixed identity of a group is a nontrivial word with constants that vanishes under every substitution of its variables. We derive lower bounds for the length of mixed identities in finite simple groups of Lie type, and characterise exactly those families of such groups of bounded rank which satisfy mixed identities of bounded length. We classify the infinite simple locally finite groups admitting a mixed identity: apart from an explicit list of alternating, finitary linear classical, and non-simply-laced groups of Lie type, no such group exists. For the groups in this list, we determine when mixed identities must be singular and obtain restrictions on their critical constants. Moreover, we prove that simple compact Lie groups do not admit mixed identities. Comments: 36 pages, 1 table Subjects: Group Theory (math.GR) MSC classes: 20F70, 20G15, 20G25, 20G40, 20G41 Cite as: arXiv:2608.14537 [math.GR] (or arXiv:2608.14537v1 [math.GR] for this version) https://doi.org/10.48550/arXiv.2608.14537 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Jakob Schneider [ view email ] [v1] Fri, 14 Aug 2026 17:51:10 UTC (39 KB) Full-text links: Access Paper: View a PDF of the paper titled Mixed identities for simple locally finite groups, by Henry Bradford and 3 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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