摘要
利用群的非空子集作成子群的充要条件,得到群G的任意一个自同构下的不动点的集合构成群G的子群.作为应用,在GL_(n)(F)上定义∗对应,计算其不动点子群.最后,利用反证法验证GL_(n)(F)上定义的∗对应其自同构类型.
The set of fixed points under any automorphism of group G form subgroups be obtained by using necessary and sufficient condition of the non-empty subsets of a group to form subgroups.As an application,the fixed point group is calculated to∗defined on GL_(n)(F).Finally,the automorphism type is comfirmed corresponding to∗defined on GL_(n)(F)by using inverse proof method.
作者
张薇
郭继东
ZhangWei;Guo Jidong(College of Mathematics and Statistics,Yili Normal University,Yining,Xinjiang 835000,China;Institute of Applied Mathematics,Yili Normal University,Yining,Xinjiang 835000,China)
出处
《伊犁师范大学学报（自然科学版）》
2023年第1期18-20,共3页
Journal of Yili Normal University：Natural Science Edition
基金
新疆维吾尔自治区自然科学基金项目(2022D01C334)
新疆维吾尔自治区高校科研计划自然科学重点项目(XJEDU2020I018).
关键词
子群
不动点子群
内自同构
外自同构
subgroup
fixed point subgroup inner automorphism
outer automorphism
