Kivanc Ersoy, Freie Universität Berlin: Groups with certain conditions on fixed points of automorphisms

Vortrag im Oberseminar der AG Algebra, Geometrie und Computeralgebra

Referent: Kivanc Ersoy, Freie Universität Berlin

Zeit: Donnerstag 07.06.2018, 17:30 Uhr

Ort: Raum 48-436

Abstract: Thompson proved that a finite group with a fixed point free automorphism of prime order is nilpotent. Later Higman, Kreknin and Kostrikin proved that in this case the nilpotency class is indeed bounded by the order of the automorphism. On the other hand, Brauer and Fowler proved that order of a finite simple group is indeed bounded in terms of the order of centralizers of involutions. Since then, there has been a lot of questions of the following type: Let G be a group with a particular type of centralizer (of fixed point set). How does the structure of the centralizer affect the structure of the group? In the first part of the talk we will give a survey of results obtained by imposing certain conditions on the centralizers. In the second part we will prove new results about finite and locally finite groups and their automorphisms.