Conway groupoids, regular two-graphs and supersimple designs

Nick Gill, Neil I. Gillespie, Cheryl E. Praeger, Jason Semeraro

    Allbwn ymchwil: Cyfraniad at gyfnodolynErthygl

    86 Wedi eu Llwytho i Lawr (Pure)


    A $2-(n,4,\lambda)$ design $(\Omega, \mathcal{B})$ is said to be supersimple if distinct lines intersect in at most two points. From such a design, one can construct a certain subset of Sym$(\Omega)$ called a "Conway groupoid". The construction generalizes Conway's construction of the groupoid $M_{13}$. It turns out that several infinite families of groupoids arise in this way, some associated with 3-transposition groups, which have two additional properties. Firstly the set of collinear point-triples forms a regular two-graph, and secondly the symmetric difference of two intersecting lines is again a line. In this paper, we show each of these properties corresponds to a group-theoretic property on the groupoid and we classify the Conway groupoids and the supersimple designs for which both of these two additional properties hold.
    Iaith wreiddiolSaesneg
    Nifer y tudalennau24
    CyfnodolynSéminaire Lotharingien de Combinatoire
    Rhif cyhoeddi79
    StatwsCyhoeddwyd - 2018

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