SEMINAR: Groups and Combinatorics Seminar: Finite groups with an automorphism inverting, squaring or cubing a non-negligible fraction of elements

Time and place: 11:00 Tuesday 23 February in Blakers LT

Speaker: Alexander Bors (University of Salzburg)

Title: Finite groups with an automorphism inverting, squaring or cubing a non-negligible fraction of elements

Abstract: There are various results in the literature stating that a finite group for which a certain parameter (e.g., the number of conjugacy classes or of prime order subgroups) is large enough must be in some sense close to being abelian. In this talk, I will present some recent results of that type on finite groups in which the maximum fraction of elements inverted resp. squared resp. cubed by a single automorphism is bounded away from 0. In spite of the elementarity of the problem, we will require some nontrivial tools for its solution, including the classification of finite simple groups and a bit of character theory.