四元数群到一类10pn阶非交换群的同态数量

吉林大学学报(理学版) ›› 2020, Vol. 58 ›› Issue (5): 1085-1092.

四元数群到一类10pⁿ阶非交换群的同态数量

李凤娇, 高百俊

伊犁师范大学数学与统计学院, 新疆伊宁 835000

收稿日期:2020-01-06 出版日期:2020-09-26 发布日期:2020-11-18
通讯作者: 高百俊 E-mail: dqgbj2008@163.com

Number of Homomorphisms from Quaternion Group to a Class of Non-Abelian Groups with Order 10pⁿ

LI Fengjiao, GAO Baijun

College of Mathematics and Statistics, Yili Normal University, Yining 835000, Xinjiang Uygur Autonomous Region, China

Received:2020-01-06 Online:2020-09-26 Published:2020-11-18

摘要/Abstract

摘要： 利用有限群论和初等数论确定一类10pⁿ阶非交换群的元素特征, 并构建四元数群到该类10pⁿ阶非交换群的所有同态映射. 通过计算这些同态映射的个数, 验证这两类群满足Asai和Yoshida猜想.

关键词: 非交换群, 四元数群, 同态数量

Abstract: By using the finite group theory and elementary number theory, we ascertained the characteristics of elements of a class of non-Abelian finite group with order 10pⁿ, and built all homomorphic mappings from quaternion group to the class of non-Abelian finite group with order 10pⁿ. We verified that those two groups could suffice the conjecture of Asai and Yoshida by calculating the number of homomorphic mapping.

Key words: non-Abelian group, quaternion group, number of homomorphisms

中图分类号:

O152.6

李凤娇, 高百俊. 四元数群到一类10pⁿ阶非交换群的同态数量[J]. 吉林大学学报(理学版), 2020, 58(5): 1085-1092.

LI Fengjiao, GAO Baijun. Number of Homomorphisms from Quaternion Group to a Class of Non-Abelian Groups with Order 10pⁿ[J]. Journal of Jilin University Science Edition, 2020, 58(5): 1085-1092.

四元数群到一类10pⁿ阶非交换群的同态数量

Number of Homomorphisms from Quaternion Group to a Class of Non-Abelian Groups with Order 10pⁿ

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