24p2q2r阶自同构群的有限Abel群G的构造
Structure of finite abelian group G with automorphism group of order 24p2q2r
王晶磊 1何立国1
作者信息
- 1. 沈阳工业大学理学院,110870,辽宁省沈阳市
- 折叠
摘要
设p、q、r为互异的奇素数,且p<q<r,G是有限Abel群,A(G)是G的自同构群.对于一个给定的有限群G,其存在唯一确定的自同构群A(G).反之,由自同构群来确定有限群的构造则是一个比较困难的问题.主要讨论了当自同构群的阶为24p2q2r时,有限Abel群G的全部类型.
Abstract
Let p,q,r be three pairwise distinct odd primes,and p<q<r.Let G be a finite abelian group,and A(G)the automorphism group of G.For a given finite group G,there is a unique and definite automorphism group A(G).Conversely,it is a difficult problem to determine the construction of a finite group by automorphism group.This research proved all types of finite abelian group G when the order of automorphism group is 24p2q2r.
关键词
自同构群/有限Abel群/欧拉函数/群结构Key words
automorphism group/finite abelian group/Euler function/structure of group引用本文复制引用
出版年
2024
国家科技期刊平台
NSTL
万方数据