Finite groups and Lie rings admitting a Frobenius group of automorphisms with fixed-point-free kernel

Khukhro, E. I. (2012) Finite groups and Lie rings admitting a Frobenius group of automorphisms with fixed-point-free kernel. In: Group Theory and Lie Theory, 19-21 March 2012, Allahabad, India. (Unpublished)

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Abstract

Suppose that a finite group $G$ admits a Frobenius group of automorphisms $FH$ with kernel $F$ and complement $H$ such that $C_G(F)=1$. 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 $|H|$). We discuss several recent results in this direction. The properties and parameters in question include the order, rank, Fitting height, nilpotency class, and the exponent.

Item Type: Conference or Workshop Item (Lecture)
Additional Information: Invited lecture
Uncontrolled Keywords: Frobenius group, nilpotent, Fitting height, exponent, Lie ring, automorphism
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 17 Nonassociative rings and algebras
MSC 2010, the AMS's Mathematics Subject Classification > 20 Group theory and generalizations
Depositing User: Professor Evgeny Khukhro
Date Deposited: 18 Oct 2012
Last Modified: 20 Oct 2017 14:13
URI: http://eprints.maths.manchester.ac.uk/id/eprint/1899

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