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 (Unpublished)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: | https://eprints.maths.manchester.ac.uk/id/eprint/1899 |
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