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2012.95: Fitting height of a finite group with a Frobenius group of automorphisms

2012.95: E. I. Khukhro (2012) Fitting height of a finite group with a Frobenius group of automorphisms.

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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 $F$ acts without non-trivial fixed points (that is, such that $C_G(F)=1$). It is proved that the Fitting height of $G$ is equal to the Fitting height of the fixed-point subgroup $C_G(H)$ and the Fitting series of $C_G(H)$ coincides with the intersections of $C_G(H)$ with the Fitting series of $G$. As a corollary, it is also proved that for any set of primes $\pi$ the $\pi$-length of $G$ is equal to the $\pi$-length of $C_G(H)$.

Item Type:MIMS Preprint
Uncontrolled Keywords:Frobenius group of automorphisms with fixed-point-free kernel; Fitting height; Clifford's theorem
Subjects:MSC 2000 > 20 Group theory and generalizations
MIMS number:2012.95
Deposited By:Professor Evgeny Khukhro
Deposited On:18 October 2012

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