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.
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页码：982 / 992
页数：11
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