| 两类非交换群之间的同态数量 |
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| 引用本文： | 李凤娇,高百俊.两类非交换群之间的同态数量[J].山东大学学报(理学版),2020,55(12):25-29. |
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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;伊犁师范大学数学与统计学院,新疆 伊宁835000 |
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| 基金项目： | 新疆维吾尔自治区自然科学基金资助项目(2017D01C419) |
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| 摘 要： | 结合代数数论的知识,计算了一类 Sylow p-子群为循环群的10pn阶非交换群之间的同态个数,以及这类群到四元数群的同态个数。作为应用,验证了这两类群是满足Asai和Yoshida猜想的。
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| 关 键 词： | 非交换群 同态数量 四元数群 |
Number of homomorphisms between two classes of non-abelian finite groups |
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| LI Feng-jiao,GAO Bai-jun.Number of homomorphisms between two classes of non-abelian finite groups[J].Journal of Shandong University,2020,55(12):25-29. |
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| Authors: | LI Feng-jiao GAO Bai-jun |
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| Institution: | College of Mathematics and Statistics, Yili Normal University, Yining 835000, Xinjiang, China |
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| Abstract: | The number of homomorphisms among a class of non-abelian groups of order 10pn with cyclic Sylow p-subgroups and from the non-abelian finite groups into quaternion group is obtained by using algebraic number theory. As an application, the number of homomorphisms of such groups satisfies the conjecture of Asai and Yoshida is verified. |
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| Keywords: | non-abelian group number of homomorphism quaternion group |
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