一类Sylow p-子群为循环群的非交换群与模群之间的同态个数  

The Number of Homomorphisms Between a Non-Comnutatire Groups with Sylow p-Subgroups as Cyclic Groups and the Modular Groups

作　　者：赵山宇 郭继东 ZHAO Shanyu;GUO Jidong(College of Mathematics and Statistics,Yili Normal University,Yining 835000,China;Institute of Applied Mathematics,Yili Normal University,Yining 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：《长春师范大学学报》2024年第6期5-10,共6页Journal of Changchun Normal University

基　　金：2022年度新疆维吾尔自治区自然科学基金项目“关于T.Asai和T.Yoshida猜想的进一步探讨”(2022D01C334)。

摘　　要：结合代数学及数论的知识,计算一类Sylow p-子群为循环群的2qp^(n)阶群与模群之间的同态个数,并验证了T.Asai和T.Yoshida猜想对此类群成立.Combining the knowledge of algebra and number theory,we calculate the number of homomorphisms between a class of Sylow p-subgroups as cyclic groups of order 2qp^(n)and the modular groups.As an application,the conjecture of T.Asai and T.Yoshida is proved to be valid for such groups.

关 键 词：非交换群 模群 群同态 T.Asai和T.Yoshida猜想 

分 类 号：O152.1[理学—数学]