Generating groups using hypergraphs

Nick P Gill, Neil I Gillespie, Anthony Nixon, Jason P G Semeraro

Research output: Contribution to journalArticle (Academic Journal)peer-review

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Abstract

To a set B of 4-subsets of a set Ω of size n, we introduce an invariant called the ‘hole stabilizer’ which generalizes a construction of Conway, Elkies and Martin of the Mathieu group M12 based on Lloyd'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 (Ω,B) with a trivial hole stabilizer, and determine all hole stabilizers associated to 2-(n,4,λ) designs with λ⩽2.
Original languageEnglish
Pages (from-to)29-52
Number of pages24
JournalQuarterly Journal of Mathematics
Volume67
Issue number1
DOIs
Publication statusPublished - 1 Mar 2016

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