On Intersections of Abelian and Nilpotent Subgroups in Finite Groups. I

被引：1

作者：

Zenkov, V. I. ^{[1
,2
]}

机构：

[1] Russian Acad Sci, Krasovskii Inst Math & Mech, Ural Branch, Ekaterinburg 620990, Russia

[2] Ural Fed Univ, Ekaterinburg 620002, Russia

来源：

PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS | 2016年 / 295卷 / 01期

基金：

俄罗斯科学基金会; 俄罗斯基础研究基金会;

关键词：

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

D O I：

10.1134/S0081543816090182

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

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 boolean AND B-g <= 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 boolean AND B-g <= F(G) for some element g from G is an almost simple group.

引用

页码：S174 / S177

页数：4