On intersections of abelian and nilpotent subgroups in finite groups. I

被引：0

作者：

V. I. Zenkov

机构：

[1] Ural Branch of the Russian Academy of Sciences,Krasovskii Institute of Mathematics and Mechanics

[2] Ural Federal University,undefined

来源：

Proceedings of the Steklov Institute of Mathematics | 2016年 / 295卷

关键词：

finite group; abelian subgroup; nilpotent subgroup; intersection of subgroups; Fitting subgroup;

D O I：

暂无

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学科分类号：

摘要：

Let A be an abelian subgroup of a finite group G, and let B be a nilpotent subgroup of G. If G is solvable, then we prove that it contains an element g such that A ∩ Bg ≤ F(G), where F(G) is the Fitting subgroup of G. If G is not solvable, we prove that a counterexample of minimal order to the conjecture that A ∩ Bg ≤ F(G) for some element g from G is an almost simple group.

引用

页码：174 / 177

页数：3