一类非交换群到四元数群的同态个数  

The Number of Homomorphisms from Non-abelian Groups to Quaternion Groups

作　　者：杨舒兰 郭继东 Yang shulan;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）》2024年第2期6-10,共5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);2021年度伊犁师范大学科研创新团队培育计划项目(CXZK2021017).

摘　　要：根据一类非交换群具有循环极大子群的有限p群的结构特征和元素的性质,给出在同构意义下5种不同类型的分类,计算此类群到四元数群的同态数量.作为应用,验证该数量关系满足T.Asai和T.Yoshida猜想.Based on the group structural characteristics and the properties elements of a class of finite p groups with cyclic maximal subgroups of non-abelian groups,five different types of classifications are given in the sense of isomorphism,and the homomorphism from this group to quaternion groups is calculated.As an application,it is verified that the quantitative relation satisfies the T.Asai and T.Yoshida conjecture.

关 键 词：极大子群 非交换群 四元数群 群同态 

分 类 号：O152.6[理学—数学]