一类亚循环群同态个数的计算  

Calculation of Number of Homomorphisms of a Class of Metacyclic Groups

作　　者：张良 海进科 ZHANG Liang;HAI Jinke(School of Mathematics and Statistics,Yili Normal University,Y ining 835000, Xinjiang Uygur Autonomous Region,China;School of Mathematics and Statistics,Qingdao University,Qingdao 266071,Sha ndong Province,China)

机构地区：[1]伊犁师范学院数学与统计分院,新疆伊宁835000 [2]青岛大学数学与统计学院,山东青岛266071

出　　处：《吉林大学学报（理学版）》2018年第5期1045-1048,共4页Journal of Jilin University:Science Edition

基　　金：山东省自然科学基金(批准号:ZR2016AM21);伊犁师范学院博士科研启动基金(批准号:2017YSBS10)

摘　　要：利用群论与同余理论,计算一类m阶循环群被4阶循环群扩张的亚循环群之间的同态个数,并给出该类亚循环群的自同态个数.所得结果验证了该类亚循环群满足Asai和Yoshida猜想.By using the group theory and congruence theory,we cal culated the number of homomorphisms betwe en a class of metacyclic groups,which were normal cyclic groups of the order m expanded by cyclic groups of the order 4,and gave the number of endomorphisms of the metacyclic grou ps.The results verified that the metacyclic groups satisfied the conjecture of Asai and Yoshida.

关 键 词：亚循环群 同态 自同态 同余 

分 类 号：O152.1[理学—数学]