A solvability criterion for finite groups

被引：0

作者：

Qian, Guo Hua ^{[1
]}

Li, Tian Ze ^{[1
]}

机构：

[1] Changshu Inst Technol, Dept Math, Changshu 215500, Peoples R China

来源：

ACTA MATHEMATICA SINICA-ENGLISH SERIES | 2016年 / 32卷 / 08期

关键词：

Finite group; solvable group; Sylow normalizer; supplement; SUBGROUPS; ADMIT;

D O I：

10.1007/s10114-016-2768-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show that if for every prime p, the normalizer of a Sylow p-subgroup of a finite group G admits a p-solvable supplement, then G is solvable. This generalizes a solvability criterion of Hall which asserts that a finite group G is solvable if and only if G has a Hall p'-subgroup for every prime p.

引用

页码：982 / 992

页数：11

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