Generating groups using hypergraphs

Gill, Nick and Gillespie, Neil and Nixon, Anthony Keith and Semeraro, Jason (2016) Generating groups using hypergraphs. The Quarterly Journal of Mathematics, 67 (1). pp. 29-52. ISSN 0033-5606

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To a set $\B$ of 4-subsets of a set $\Omega$ of size $n$ we introduce an invariant called the `hole stabilizer' which generalises a construction of Conway, Elkies and Martin of the Mathieu group $M_{12}$ based on Loyd's `15-puzzle'. It is shown that hole stabilizers may be regarded as objects inside an objective partial group (in the sense of Chermak). We classify pairs $(\Omega,\B)$ with a trivial hole stabilizer, and determine all hole stabilizers associated to $2$-$(n,4,\lambda)$ designs with $\lambda \leq 2$.

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Journal Article
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The Quarterly Journal of Mathematics
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This is a pre-copy-editing, author-produced PDF of an article accepted for publication in The Quarterly Journal of Mathematics following peer review. The definitive publisher-authenticated version Nick Gill, Neil I. Gillespie, Anthony Nixon, and Jason Semeraro GENERATING GROUPS USING HYPERGRAPHS Q J Math (2016) 67 (1): 29-52 doi:10.1093/qmath/haw001 is available online at:
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08 Mar 2016 16:00
Last Modified:
21 Sep 2023 02:00