Rank and order of a finite group admitting a Frobenius group of automorphisms
نویسنده
چکیده
Suppose that a finite group G admits a Frobenius group of automorphisms FH of coprime order with kernel F and complement H. In the case where G is a finite p-group 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 fixed-point subgroup CG(H) of the complement, and the rank of G is bounded above in terms of |H| and the rank of CG(H). Earlier such results were known under the stronger assumption that the kernel F acts on G fixed-point-freely. As a corollary, in the case where G is an arbitrary finite group with a Frobenius group of automorphisms FH of coprime order with kernel F and complement H, estimates are obtained of the form |G| 6 |CG(F )| · f(|H|, |CG(H)|) for the order, and r(G) 6 r(CG(F )) + g(|H|, r(CG(H))) for the rank, where f and g are some functions of two variables. to Victor Danilovich Mazurov on his 70th birthday
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تاریخ انتشار 2013