Generating groups using hypergraphs

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

Allbwn ymchwil: Cyfraniad at gyfnodolynErthygladolygiad gan gymheiriaid

74 Wedi eu Llwytho i Lawr (Pure)

Crynodeb

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.
Iaith wreiddiolSaesneg
Tudalennau (o-i)29-52
Nifer y tudalennau24
CyfnodolynQuarterly Journal of Mathematics
Cyfrol67
Rhif cyhoeddi1
Dynodwyr Gwrthrych Digidol (DOIs)
StatwsCyhoeddwyd - 7 Maw 2016

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