Russ Woodroofe: Invariable generation of alternating groups

Russ Woodroofe (University of Primorska): Invariable generation of alternating groups Abstract: A group is invariably generated by two elements if it is generated by any pair of conjugates of the respective elements. Which finite simple groups are invariably generated by two elements of prime order? For alternating groups, this condition fails infinitely often, as Shareshian and I showed in joint work a few years ago. In ongoing work with Guralnick and Shareshian, we show computationally that A_n is generated by an element of prime order together with one of prime power order for all n at most one trillion. Our approach combines results from finite group theory with results and approaches from computational number theory.