The spread of a finite group

Abstract: Many interesting and surprising results have arisen from studying generating sets for groups. For example, every finite simple group has a generating pair, and moreover Guralnick and Kantor proved that in a finite simple group every nontrivial element is contained in a generating pair. This talk will focus on recent work with Burness and Guralnick, that completely classifies the finite groups where every nontrivial element is contained in a generating pair and thus settles a 2008 conjecture of Breuer, Guralnick and Kantor. I will also give a graph theoretic interpretation of the topic, highlight how our work answers a 1975 question of Brenner and Wiegold and discuss what is known for infinite groups.

group theoryrings and algebras

Audience: researchers in the topic

Al@Bicocca take-away