一类不能作为自同构群的奇阶群

李世荣

数学学报 ›› 1996, Vol. 39 ›› Issue (4)

PDF(438 KB)
PDF(438 KB)
数学学报 ›› 1996, Vol. 39 ›› Issue (4) DOI: 10.12386/A1996sxxb0077
论文

一类不能作为自同构群的奇阶群

    李世荣
作者信息 +

Some Groups of Odd Order Which Cannot Function as Automorphism Groups

Author information +
文章历史 +

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.

Abstract

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.

关键词

全自同构群 / 对合自同构 / 有限群

引用本文

导出引用
李世荣. 一类不能作为自同构群的奇阶群. 数学学报, 1996, 39(4) https://doi.org/10.12386/A1996sxxb0077
Some Groups of Odd Order Which Cannot Function as Automorphism Groups. Acta Mathematica Sinica, Chinese Series, 1996, 39(4) https://doi.org/10.12386/A1996sxxb0077
PDF(438 KB)

340

Accesses

0

Citation

Detail

段落导航
相关文章

/