摘要
本文研究了每个子群为拟正规或自正规的有限群,给出了这类群的完全分类,主要结果为定理G的每个子群为拟正规或自正规当且仅当G为下列情形之一:Ⅰ)G为拟Hamilton群,Ⅱ)G=HP,其中H为G的正规abelianp'-Hall子群.P=〈x〉∈Syl_p(G)。〈x ̄p〉=O_p(G)=Z(G),x在H上诱导H的一个p阶无不动点的幂自同构.p为|G|的最小素因子。由此定理可得文[1]所获得的定理。
In this paper authors study such a finite group in which each subgroup is eitherquasinormal or selfuormal and characterize this kind of finite groups. The main result is Theorem Every subgroup of group G is either quasinormal or selfuormal if and only ifG is precisely one of the followingⅠ)G is a quasi-Hamilton group.Ⅱ)G=HP, where H is a normal abelian p'-Hall subgrou.P=〈x〉∈Syl_p(G),〈x ̄p〉=O_p(G)=Z(G)and x induces a fixed-point-free power automorphisim of order p on H. p is thesmallest prime factor of |G|.The theorem in paper[1]can be obtained by the above theorem.
出处
《数学学报(中文版)》
SCIE
CSCD
北大核心
1995年第3期381-385,共5页
Acta Mathematica Sinica:Chinese Series
基金
山西省青年科学基金
关键词
拟正规子群
自正规子群
子群
有限群
quasinormal subgroup,selfnormal subgroup,fixed-point-free power automorphism,Inner abelian group