2015/10/22 by Nick Gill, Neil I. Gillespie, Gill, Nick +5
Biochemistry, Genetics and Molecular Biology · Engineering · Mathematics · #05B05 #20B15 #20B25 #Chromatin Remodeling and Cancer #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #graph theory and CDMA systems #math.GR #msc:05B05 #msc:20B15 #msc:20B25
paper · pdf · doi:10.48550/arxiv.1510.06680
17 pages
arxiv created 2015/10/22 · openalex publication_date 2015/10/22 · arxiv updated 2015/10/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A 2-(n,4,λ) design (Ω, 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(Ω) called a "Conway groupoid". The construction generalizes Conway's construction of the groupoid M13. 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.