分配子及其应用  

Distributors and Their Applications

作　　者：杨雨泽 海进科 YANG Yuze;HAI Jinke(School of Mathematics and Statistics,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,新疆伊宁835000

出　　处：《吉林大学学报(理学版)》2025年第2期360-366,共7页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:12471021)。

摘　　要：首先,通过引入群的分配子概念,给出群分配子的若干性质;其次,对群论中换位子和p-换位子的相应结果进行推广,并证明群G到群H的映射f为群同态当且仅当群G的f-分配子是1;最后,作为应用,计算出一类亚循环群到二面体群之间的同态个数.Firstly,by introducing the notion of distributors of groups,we give some properties of distributors of groups.Secondly,we generalize the corresponding results of commutators and p-commutato rs in group theory,and prove that the mapping f from group G to group H is a group homomorphism if and only if the f-distributor of group G is 1.Finally,as an application,we calculate the number of homomorphisms from a class of metacyclic groups to dihedral groups.

关 键 词：分配子 p-换位子 p-导群 群同态 

分 类 号：O152.1[理学—数学]