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

Khukhro, Evgeny (2012) Fitting height of a finite group with a Frobenius group of automorphisms. Journal of Algebra, 366 . pp. 1-11. ISSN 0021-8693

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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 nontrivial 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 � the �-length of G is equal to the �-length of C G(H). © 2012 Elsevier Inc.

Keywords:Automorphism, Fitting height, Fixed-point-free, Frobenius group, Soluble
Subjects:G Mathematical and Computer Sciences > G100 Mathematics
Divisions:College of Science > School of Mathematics and Physics
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ID Code:15581
Deposited On:12 Nov 2014 15:42

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