两类特殊亚循环群之间的同态数量  

Number of Homomorphisms between Two Classes of Special Metacyclic Groups

作　　者：任小强 高百俊 REN Xiaoqiang;GAO Baijun(School of Mathematics and Statistics,Institute of Applied Mathematics,Yili Normal University,Yining 835000,Xinjiang Uygur Autonomous Region,China)

机构地区：[1]伊犁师范大学数学与统计学院,应用数学研究所,新疆伊宁835000

出　　处：《吉林大学学报（理学版）》2023年第1期66-72,共7页Journal of Jilin University:Science Edition

基　　金：新疆维吾尔自治区天山青年人才项目(批准号:2020Q023);伊犁师范大学博士科研启动项目(批准号:2020YSBS010)。

摘　　要：利用初等数论的基本知识,研究一类10 p^(n)阶亚循环群H=〈a,b |a^(10)=1=b p^(n),a^(-1) ba=b r,r≠ 1(mod p^(n)),r^(5)≡1(mod p^(n)),p≡1(mod 5)〉的元素特征,计算其与亚循环群G_(m)=〈x〉×〈y〉=〈x,y |x^(m)=1=y 4,y^(-1) xy=x^(-1)〉之间的同态数量,并验证其同态数量满足[WTBZ]Asai和Yoshida猜想.By using the basic knowledge of elementary number theory,we studied the element characteristics of a class of metacyclic groups H=〈a,b |a^(10)=1=b p^(n),a^(-1) ba=b r,r≠ 1(mod p^(n)),r^(5)≡1(mod p^(n)),p≡1(mod 5)〉of order 10 p^(n),calculated the number of homomorphisms between H and metacyclic groups G_(m)=〈x〉×〈y〉=〈x,y |x^(m)=1=y 4,y^(-1) xy=x^(-1)〉,and verified that the number of homomorphisms between the two groups satisfied the conjecture of Asai and Yoshida.

关 键 词：亚循环群 同态数量 Asai和Yoshida猜想 

分 类 号：O152.6[理学—数学]