Ercan, G., Guloglu, I. and Khukhro, Evgeny (2014) Rank and order of a finite group admitting a Frobeniuslike group of automorphisms. Algebra and Logic, 53 (3). pp. 258265. ISSN 00025232
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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 with a nontrivial complement H such that FH/[F,F] is a Frobenius group with Frobenius kernel F/[F,F]. Suppose that a finite group G admits a Frobeniuslike group of automorphisms FH of coprime order with certain additional restrictions (which are satisfied, in particular, if either FH is odd or H = 2). In the case where G is a finite pgroup such that G = [G, F] it is proved that the rank of G is bounded above in terms of H and the rank of the fixedpoint subgroup C G (H), and that G is bounded above in terms of H and C G (H). As a corollary, in the case where G is an arbitrary finite group estimates are obtained of the form G ≤C G (F) · f(H, C G (H)) for the order, and r(G) ≤ r(C G (F)) + g(H, r(C G (H))) for the rank, where f and g are some functions of two variables.
Additional Information:  Translated from Algebra i Logika, Vol. 53, No. 3, pp. 401412, MayJune, 2014. 

Keywords:  Automorphism, Finite group, Frobenius group, rank, order, JCNotOpen 
Subjects:  G Mathematical and Computer Sciences > G100 Mathematics 
Divisions:  College of Science > School of Mathematics and Physics 
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ID Code:  16200 
Deposited On:  05 Dec 2014 09:57 
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