| 四元数群到一类10pn阶非交换群的同态数量 |
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| 引用本文： | 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), 2021, 58(5): 1085-1092 |
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| 作者姓名： | 李凤娇 高百俊 |
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| 作者单位： | 伊犁师范大学 数学与统计学院, 新疆 伊宁 835000 |
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| 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.
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| 关 键 词： | 非交换群 四元数群 同态数量 |
| 收稿时间： | 2020-01-06 |
Number of Homomorphisms from Quaternion Group to a Class of Non-Abelian Groups with Order 10pn |
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| 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: Sci Ed, 2021, 58(5): 1085-1092 |
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| Authors: | LI Fengjiao GAO Baijun |
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| Affiliation: | College of Mathematics and Statistics, Yili Normal University, Yining 835000, Xinjiang Uygur Autonomous Region, China |
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| 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. |
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| Keywords: | non-Abelian group quaternion group number of homomorphisms |
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