二面体群到一类亚循环群之间的同态个数

doi:10.6040/j.issn.1671-9352.0.2018.362

《山东大学学报(理学版)》 ›› 2019, Vol. 54 ›› Issue (6): 34-40.doi: 10.6040/j.issn.1671-9352.0.2018.362

• • 上一篇

二面体群到一类亚循环群之间的同态个数

李红霞¹,郭继东^1*,海进科^1,2

1.伊犁师范大学数学与统计分院, 新疆伊宁835000;2.青岛大学数学与统计学院, 山东青岛 266071

发布日期:2019-06-05
作者简介:李红霞(1994— ),女,硕士研究生,研究方向为有限群理论. E-mail:1484818252@qq.com*通信作者简介:郭继东(1965— ),男,博士研究生,教授,研究方向为有限群理论. E-mail:guojd662@163.com
基金资助:
新疆维吾尔自治区“十三五“重点学科(数学)开放课题(XJZDXK-M201708)

The number of homomorphisms from dihedral groups to a class of metacyclic groups

LI Hong-xia¹, GUO Ji-dong^1*, HAI Jin-ke^1,2

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

Published:2019-06-05

摘要/Abstract

摘要： 基于群理论中亚循环群的结构以及该群元素的特征,利用代数学及数论的基本方法,具体地计算出二面体群到一类亚循环群之间的同态个数。作为应用,验证了T.Asai 和T.Yoshdia猜想对此类亚循环群成立。

关键词: 二面体群, 亚循环群, 群同态

Abstract: Based on the theory group of the structure of metacyclic group and characteristics of the group elements, by using the basic method of algebra and number theory, it is calculated that the number of homomorphism between dihedral groups and a class of metacyclic groups. As an application, it verifies that T.Asai and T.Yoshidas conjectures establish such a cyclic group.

Key words: dihedral group, metacyclic group, homomorphism

中图分类号:

O152.6

李红霞,郭继东,海进科. 二面体群到一类亚循环群之间的同态个数[J]. 《山东大学学报(理学版)》, 2019, 54(6): 34-40.

LI Hong-xia, GUO Ji-dong, HAI Jin-ke. The number of homomorphisms from dihedral groups to a class of metacyclic groups[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(6): 34-40.

参考文献

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二面体群到一类亚循环群之间的同态个数

The number of homomorphisms from dihedral groups to a class of metacyclic groups

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