一类模群到亚循环群的同态个数  

The Number of Homomorphisms from a Class Modular Groups to Metacyclic Groups

作　　者：王知真 郭继东 WANG Zhi-zhen;GUO Ji-dong(College of Mathematics and Statistics,Yili Normal Universtity,Yining 835000,Xinjiang,China;Institute of Applied Mathematics,Yili Normal Universtity,Yining 835000,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：《喀什大学学报》2023年第6期18-23,共6页Journal of Kashi University

基　　金：新疆维吾尔自治区自然科学基金项目“关于T.Asai和T.Yoshida猜想的进一步探论”(2022D01C334);伊犁师范大学科研创新团队培育计划项目“有限群结构理论及应用”(CXZ2021017).

摘　　要：基于群理论下的两类非交换群的结构以及元素的阶,利用代数学及初等数论的基本方法,计算模群到2nq阶亚循环群的同态个数,并通过实例验证T.Asai&T.Yoshida猜想对此类群成立.Based on the group structure and the order of elements of two classes of non-abelian groups in group theory,the number of homomorphisms from modular groups to metacyclic groups of order 2nq by using basic methods of algebra and elementary number theory.As an application,the number of homomorphisms of such groups satisfies the conjecture of T.Asai&T.Yoshida is varified.

关 键 词：模群 亚循环群 群同态 T.Asai&T.Yoshida猜想 

分 类 号：O152.1[理学—数学]