# Evgeny Khukhro giving a talk in Bristol

Evgeny Khukhro is giving a talk “*Finite groups with Frobenius groups of automorphisms*” at Bristol University Algebra & Geometry Seminar, 17 June 2015, 2.30 PM

http://www.bristol.ac.uk/maths/events/2015/evgeny-khukhro.html

Abstract: Suppose that a finite group *G* admits a Frobenius group of automorphisms *FH* with kernel *F* and complement *H* such that *C*_{G}(*F*)* = *1. The condition *C*_{G}(*F*) = 1 alone already implies that *G* is soluble and has Fitting height bounded in terms of *F*. Finer results on the structure of *G* can be derived by using the “additional” action of *H*. There are good reasons to expect many properties and parameters of *G* to be close to the same properties and parameters of *C*_{G}(*H*) (possibly, also depending on |*H*|). Examples of such properties and parameters include the order, rank, Fitting height, nilpotency class, and exponent. I will discuss several recent results in this direction, as well as generalizations and open problems. Results concerning bounding the order, sectional rank, and Fitting height of *G* are based on representation theory. Various Lie ring methods are used for bounding the nilpotency class and exponent of *G*.

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