一类素数幂阶J群到其商群的同态个数  

The Number of Homorphisms from a Class of Prime Power Order J-Groups to Its Quotient Group

作　　者：蒋鹏程 郭继东 Jiang Pengcheng;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4期10-13,共4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：给出了一类素数幂阶J群其元素的构造,讨论关于其换位子群作成的商群结构,建立该群到其商群的同态映射集合与商群自同态集合之间的同构映射,计算后者的数量满足T.Asai和T.Yoshida猜想,间接地验证前者的数量也满足该猜想.The construction of the elements of a class of prime power-order J-groups is given,discusses the structure of the quotient group of J-groups by its commutator subgroup,establishes an isomorphism map between the set of J-group to its quotient group and the endomorphism set of the quotient group,calculates the number of the latter satisfies the conjectures of T.Asai and T.Yoshida,and indirectly verifies that the number of the former also satisfies the conjecture.

关 键 词：素数幂阶J群 商群 同态数量 

分 类 号：O152.1[理学—数学]