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    Rights statement: 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: http://qjmath.oxfordjournals.org/content/67/1/29.abstract

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Generating groups using hypergraphs

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<mark>Journal publication date</mark>7/03/2016
<mark>Journal</mark>The Quarterly Journal of Mathematics
Issue number1
Volume67
Number of pages24
Pages (from-to)29-52
Publication StatusPublished
<mark>Original language</mark>English

Abstract

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 $\lambda \leq 2$.

Bibliographic note

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: http://qjmath.oxfordjournals.org/content/67/1/29.abstract