Khukhro, E. I.
(2012)
*Fitting height of a finite group with a Frobenius group of automorphisms.*
[MIMS Preprint]

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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 |
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Uncontrolled Keywords: | Frobenius group of automorphisms with fixed-point-free kernel; Fitting height; Clifford's theorem |

Subjects: | 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: | 08 Nov 2017 18:18 |

URI: | http://eprints.maths.manchester.ac.uk/id/eprint/1895 |

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