不动点子群及GL_(n)(F)上∗的自同构类型  

Fixed Point Group and Automorphism Type of∗on GL_(n)(F)

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)

机构地区：[1]伊犁师范大学数学与统计学院,新疆伊宁835000 [2]伊犁师范大学应用数学研究所,新疆伊宁835000

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).

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.

关 键 词：子群 不动点子群 内自同构 外自同构 

分 类 号：O152.6[理学—数学]