亚循环群到亚循环群之间的同态个数

doi:10.6040/j.issn.1671-9352.0.2017.562

山东大学学报（理学版） ›› 2018, Vol. 53 ›› Issue (6): 17-22.doi: 10.6040/j.issn.1671-9352.0.2017.562

亚循环群到亚循环群之间的同态个数

张良¹,海进科^1,2*

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

收稿日期:2017-10-31 出版日期:2018-06-20 发布日期:2018-06-13
作者简介:张良(1979— ), 男, 博士, 讲师, 研究方向为群与代数编码. E-mail:zhangliang0819@aliyun.com*通信作者简介:海进科(1964— ), 男, 博士, 教授, 研究方向为有限群及其表示. E-mail:haijinke2002@aliyun.com
基金资助:
山东省自然科学基金资助项目(ZR2016AM21);伊犁师范学院博士基金项目(2017YSBS10)

The number of homomorphisms from metacyclic groups to metacyclic groups

1. College of Mathematics and Statistics, Yili Normal University, Yining 835000, Xinjiang, China;
2. College of Mathematics and Statistics, Qingdao University, Qingdao 266071, Shandong, China

Received:2017-10-31 Online:2018-06-20 Published:2018-06-13

摘要/Abstract

摘要： 计算了一类m阶循环群通过2p阶循环群扩张的亚循环群之间的同态个数, 并给出了此类亚循环群自同态半群的阶。作为应用,验证了T. Asai和T. Yohsdia猜想对此类亚循环群成立。

关键词: 亚循环群, 群同态, 同余关系

Abstract: The number of homomorphisms between a class of metacyclic groups, which are normal cyclic groups of the order m extended by cyclic groups of the order 2p, is calculated, and the number of endomorphisms of such groups is obtained. As an application, the number of homomorphisms of such groups satisfies the conjecture of T.Asai and T.Yohsdia is varified.

Key words: metacyclic group, homomorphism, congruence relation

中图分类号:

O152.6

张良,海进科. 亚循环群到亚循环群之间的同态个数[J]. 山东大学学报（理学版）, 2018, 53(6): 17-22.

参考文献

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亚循环群到亚循环群之间的同态个数

The number of homomorphisms from metacyclic groups to metacyclic groups

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