Nilpotent length of a finite group admitting a frobenius group of automorphisms with fixed-point-free kernel

被引:0
作者
E. I. Khukhro
机构
[1] Russian Academy of Sciences,Sobolev Institute of Mathematics, Siberian Branch
来源
Algebra and Logic | 2011年 / 49卷
关键词
Frobenius group; automorphism; finite group; soluble group; nilpotent length; Fitting series;
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学科分类号
摘要
Suppose that a finite group G admits a Frobenius group FH of automorphisms with kernel F and complement H such that the fixed-point subgroup of F is trivial, i.e., CG(F) = 1, and the orders of G and H are coprime. It is proved that the nilpotent length of G is equal to the nilpotent length of CG(H) and the Fitting series of the fixed-point subgroup CG(H) coincides with a series obtained by taking intersections of CG(H) with the Fitting series of G.
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页码:551 / 560
页数:9
相关论文
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