二面体群到有限群的同态个数  

The number of homomorphisms from dihedral groups to any finite groups

作　　者：谭婕 张良 郭继东 TAN Jie;ZHANG Liang;GUO Jidong(School of Mathematics and Statistics,Yili Normal University,Yining 835000,Xinjiang,China;Institute of Applied Mathematics,Yili Normal University,Yining 835G00,Xinjiang,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：《山东大学学报（理学版）》2023年第6期31-34,共4页Journal of Shandong University(Natural Science)

基　　金：新疆高校科研计划项目(XJEDU2019045);伊犁州科技计划项目(YZ2022D004)。

摘　　要：研究二面体群的自同构群和正规子群,得到二面体群到任意有限群的同态个数满足的数量关系。作为应用,验证Asai和Yoshida猜想对二面体群成立。Automorphism groups and normal subgroups of dihedral groups are studied,and the number of homomorphisms from dihedral groups to any finite group is obtained.As an application of this result,the conjecture of Asai and Yoshida is verified for dihedral groups.

关 键 词：二面体群 群同态个数 自同构群 

分 类 号：O152.1[理学—数学]