Groups satisfying Gaschütz's complement theorem

[2608.27579] Groups satisfying Gaschütz's complement theorem Skip to main content Search Submit Donate Log in Mathematics > Group Theory arXiv:2608.27579 (math) [Submitted on 27 Aug 2026] Title: Groups satisfying Gaschütz's complement theorem Authors: Stefanos Aivazidis , Benjamin Sambale View PDF HTML (experimental) Abstract: A classical theorem of Gaschütz states that an abelian normal subgroup N of a finite group G has a complement in G whenever it has a complement in some subgroup H with $N \leq H \leq G$ and gcd(|N|, [G:H]) = 1. We characterize the finite groups N for which this theorem remains valid without the abelian hypothesis: this is the case if and only if $Z(N) \cap N' = 1$ and N has a complement in a quotient of the holomorph Hol(N) by a diagonal copy of N'. This completes a previous paper by the second author. Comments: 7 pages Subjects: Group Theory (math.GR) Cite as: arXiv:2608.27579 [math.GR] (or arXiv:2608.27579v1 [math.GR] for this version) https://doi.org/10.48550/arXiv.2608.27579 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Benjamin Sambale [ view email ] [v1] Thu, 27 Aug 2026 18:06:34 UTC (9 KB) Full-text links: Access Paper: 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 SciX Google Scholar Semantic Scholar export BibTeX citation 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)

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