Khukhro, Evgeny (2013) Rank and order of a finite group admitting a Frobenius group of automorphisms. Algebra and Logic, 52 (1). pp. 7278. ISSN 00025232
Full content URL: http://link.springer.com/article/10.1007%2Fs10469...
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Abstract
Suppose that a finite group G admits a Frobenius group FH of automorphisms of coprime order with kernel F and complement H. For the case where G is a finite pgroup such that G = G, F, it is proved that the order of G is bounded above in terms of the order of H and the order of the fixedpoint subgroup C G(H) of the complement, while the rank of G is bounded above in terms of H and the rank of C G(H). Earlier, such results were known under the stronger assumption that the kernel F acts on G fixedpointfreely. As a corollary, for the case where G is an arbitrary finite group with a Frobenius group FH of automorphisms of coprime order with kernel F and complement H, estimates are obtained which are of the formG ≤ C G (F) · f(H, C G (H)) for the order, and of the form 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. © 2013 Springer Science+Business Media New York.
Additional Information:  Translated from Algebra i Logika, Vol. 52, No. 1, pp. 99108, JanuaryFebruary, 2013. 

Keywords:  Automorphism, Finite group, Frobenius group, Order, pgroup, Rank 
Subjects:  G Mathematical and Computer Sciences > G110 Pure Mathematics 
Divisions:  College of Science > School of Mathematics and Physics 
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ID Code:  15577 
Deposited On:  28 Oct 2014 10:13 
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