SEMINAR: Groups and Combinatorics Seminar: Conway Groupoid

Time and place: 15:00 Friday 10 April in Weatherburn LT.

Speaker: Jason Semeraro (University of Bristol)

Title: Conway Groupoids.

Abstract: To a supersimple 2-(n,4,lambda) design (a simple design where lines intersect in at most two points), one may associate a "Conway groupoid." This is a generalization of the Mathieu groupoid associated to Conway's M_13 using a `game' played on P_3, the finite projective plane of order 3. We will discuss what is known so far about Conway groupoids. Highlights include a full classification for lambda<3, a structural characterization of the Mathieu groupoid, and a surprising connection with 3-transposition groups. We also speculate on the possibility of a full classification subject to the condition that the analogue of the set M_13 actually forms a group. If time permits, we will describe a new infinite family of completely transitive codes which were discovered along the way. The talk is intended to be accessible, with plenty of time given to motivation and context. This is joint work with Nick Gill and Neil Gillespie.