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Generating groups using hypergraphs

Research output: Contribution to journalArticle

  • Nick P Gill
  • Neil I Gillespie
  • Anthony Nixon
  • Jason P G Semeraro
Original languageEnglish
Pages (from-to)29-52
Number of pages24
JournalQuarterly Journal of Mathematics
Issue number1
DateAccepted/In press - 18 Dec 2015
DatePublished (current) - 1 Mar 2016


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.

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