Generating groups using hypergraphs

Nick Gill, Neil I. Gillespie, Anthony Nixon, Jason Semeraro

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To a set B of 4-subsets of a set 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 (,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
Issue number1
Publication statusPublished - 7 Mar 2016


  • math.GR
  • 20B15, 20B25, 05B05


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