Khukhro, Evgeny and Makarenko, N Yu. (2013) Finite groups and Lie rings with a metacyclic Frobenius group of automorphisms. Journal of Algebra, 386 . pp. 77104. ISSN 00218693
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Item Type:  Article 

Item Status:  Live Archive 
Abstract
Suppose that a finite group G admits a Frobenius group of automorphisms FH of coprime order with cyclic kernel F and complement H such that the fixedpoint subgroup C G(H) of the complement is nilpotent of class c. It is proved that G has a nilpotent characteristic subgroup of index bounded in terms of c, C G(F), and F whose nilpotency class is bounded in terms of c and H only. This generalizes the previous theorem of the authors and P. Shumyatsky, where for the case of C G(F) = 1 the whole group was proved to be nilpotent of (c, H)bounded class. Examples show that the condition of F being cyclic is essential. Results based on the classification provide reduction to soluble groups. Then representation theory arguments are used to bound the index of the Fitting subgroup. Lie ring methods are used for nilpotent groups. A similar theorem on Lie rings with a metacyclic Frobenius group of automorphisms FH is also proved. © 2013 Elsevier Inc.
Keywords:  Finite group, Frobenius group, Automorphism, Soluble, Nilpotent, Clifford's theorum, Lie ring 

Subjects:  G Mathematical and Computer Sciences > G110 Pure Mathematics 
Divisions:  College of Science > School of Mathematics and Physics 
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ID Code:  15576 
Deposited On:  28 Oct 2014 10:24 
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