A Solvability Criterion for Finite Groups  

作　　者：Guo Hua QIAN Tian Ze LI 

机构地区：[1]Department of Mathematics,Changshu Institute of Technology

出　　处：《Acta Mathematica Sinica,English Series》2016年第8期982-992,共11页数学学报（英文版）

基　　金：supported by NSFC(Grant No.11471054);supported by NSFC(Grant No.11101055)

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 C is solvable if and only if G has a Hall p/-subgroup for every prime p.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 C is solvable if and only if G has a Hall p/-subgroup for every prime p.

关 键 词：Finite group solvable group Sylow normalizer SUPPLEMENT 

分 类 号：O152.1[理学—数学]