摘要
本文考虑如下问题:怎样的有限群可以作为另一个有限群的全自同构群?我们首先证明,若有限群K有一个正规Sylowp-子群使得|K:Z(K)|p=p2,那么K有2阶自同构.利用这个结果,我们证明了,若奇阶群G具有阶Psm(1≤s≤3),p为|G|的最小素因子,pm,m无立方因子,则G不可能作为全自同构群.
The following problem is considered: what kind of finite groups can function as fullautomorphism group of a finite group? We first show that if the finite group K has a normalSylow p-subgroup such that |K/Z(K)|p=p2, then K has an automorphism of order 2. Usingthis result, we have shown that if G is an odd order group with order psm (1 ≤s ≤3), wherep is the smallest prime divisor of |G|, p m and m is cubefree, then G cannot function as fullautomorphism group.
出处
《数学学报(中文版)》
SCIE
CSCD
北大核心
1996年第4期524-530,共7页
Acta Mathematica Sinica:Chinese Series
基金
国家自然科学基金
广西自然科学基金