有限循环群上奇素数次方根态射的个数  

Number of the Odd Prime-th Root Morphisms of a Finite Cyclic Group

作　　者：韩乙飞 HAN Yifei(School of Mathematics and Statistics Science,Fujian Normal University,Fuzhou,Fujian 350007)

机构地区：[1]福建师范大学数学与统计学院,福建福州350007

出　　处：《武夷学院学报》2024年第3期6-8,共3页Journal of Wuyi University

摘　　要：设G为m阶有限循环群,m>1,φ:G→G为群同态。若φ^(k)=1_(G),1_(G)为恒等态射,k为正整数,称φ为G的k次方根态射,求出当k为奇素数时G的k次方根态射的个数。Let G be a finite cyclic group of order m,m>1,φ:G→G be a group homomorphism.If φ^(k)=1_(G),where 1_(G) is the identity morphism,and k is a positive integer,thenφis called the k-th root morphisms of G.In this paper,we determine the number of k-th root morphisms of G if k is an odd prime number.

关 键 词：有限循环群 k次方根态射 个数 

分 类 号：O152.1[理学—数学]