Ercan, Gulin and Guloglu, Ismail S. and Khukhro, Evgeny (2014) Derived length of a Frobeniuslike kernel. Journal of Algebra, 412 . pp. 179188. ISSN 00218693
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Item Type:  Article 

Item Status:  Live Archive 
Abstract
A finite group FH is said to be Frobeniuslike if it has a nontrivial nilpotent normal subgroup F called kernel which has a nontrivial complement H such that F H/F, F is a Frobenius group with Frobenius kernel F/F, F. Suppose that a Frobeniuslike group FH acts faithfully by linear transformations on a vector space V over a field of characteristic that does not divide F H. It is proved that the derived length of the kernel F is bounded solely in terms of the dimension m = dimC V(H) of the fixedpoint subspace of H by g(m) = 3 + log2(m + 1). It follows that if a Frobeniuslike group FH acts faithfully by coprime automorphisms on a finite group G, then the derived length of the kernel F is at most g(r), where r is the sectional rank of C G(H). As an application, for a finite solvable group G admitting an automorphism φ of prime order coprime to G, a bound for the plength of G is obtained in terms of the rank of a Hall p 'subgroup of C G(φ). Earlier results of this kind were known only in the special case when the complement of the acting Frobeniuslike group was assumed to have prime order and its fixedpoint subspace (or subgroup) was assumed to be onedimensional (or have all Sylow subgroups cyclic). © 2014.
Keywords:  Frobeniuslike group, Derived length, Fixed points, JCNotOpen 

Subjects:  G Mathematical and Computer Sciences > G100 Mathematics G Mathematical and Computer Sciences > G110 Pure Mathematics 
Divisions:  College of Science > School of Mathematics and Physics 
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ID Code:  15574 
Deposited On:  27 Oct 2014 12:44 
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