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;

D O I：

暂无

中图分类号：

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.

引用

页码：551 / 560

页数：9

共 10 条

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[9] Hartley B(undefined)Fixed points of the complements of Frobenius groups of automorphisms undefined undefined undefined-undefined
[10] Khukhro EI(undefined)undefined undefined undefined undefined-undefined

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