SEMINAR: Groups and Combinatorics Seminar: The spread of a finite group

Groups and Combinatorics Seminar

Simon Guest (UWA)

will speak on

The spread of a finite group

at 1pm on Friday 14th of October in MLR2

Abstract: Let G be a finite group. We say that G has spread at least k if for any k distinct nontrivial elements x_1, ... , x_k in G, there exists y in G such that x_i and y generate G for each i. If G does not have spread at least 1 then G is said to have spread 0. Using elementary methods we can prove that if G has a non-trivial normal subgroup N such that G/N is non-cyclic then G must have spread 0. It has been conjectured by Guralnick and Kantor that the converse is true. They can prove that the converse holds in many cases. We will discuss some recent joint work with Tim Burness involving the remaining cases.