Abstract for the talk on 10.01.2019 (11:00 h)Seminar on Nonlinear Algebra
Mima Stanojkovski (Universität Bielefeld)
Intense automorphisms of finite groups
Let G be a finite group and let Int(G) be the subgroup of Aut(G) consisting of those automorphisms (called 'intense') that send each subgroup of G to a conjugate. Intense automorphisms arise naturally as solutions to a problem coming from Galois cohomology, still they give rise to a greatly entertaining theory on its own. We will discuss the case of groups of prime power order and see that, if G has prime power order but Int(G) does not, then the structure of G is (surprisingly!) almost completely determined by its nilpotency class. The results I will present are part of my PhD thesis, which I wrote under the supervision of Prof. Hendrik Lenstra at the University of Leiden.