| 一类非交换群的自同态和自同构数量 |
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| 引用本文： | 张维,郭继东,张良. 一类非交换群的自同态和自同构数量[J]. 山东大学学报(理学版), 2023, 58(2): 13-19. DOI: 10.6040/j.issn.1671-9352.0.2022.058 |
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| 作者姓名： | 张维 郭继东 张良 |
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| 作者单位： | 伊犁师范大学 1.数学与统计学院;2.应用数学研究所, 新疆 伊宁 835000 |
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| 基金项目： | 新疆维吾尔自治区高校科研计划自然科学重点项目(XJEDU2020I018) |
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| 摘 要： | 基于群理论下一类非交换群的群结构以及元素的阶,计算一类Sylow p-子群为循环群的2qpn(q为奇素数)阶非交换群的自同态个数和自同构个数,并验证其自同态个数满足T.Asai和T.Yoshida 猜想。
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| 关 键 词： | 非交换群 自同态 自同构 T.Asai & T.Yoshida猜想 |
The number of endomorphisms and automorphisms of a class of non-abelian groups |
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| ZHANG Wei,GUO Ji-dong,ZHANG Liang. The number of endomorphisms and automorphisms of a class of non-abelian groups[J]. Journal of Shandong University, 2023, 58(2): 13-19. DOI: 10.6040/j.issn.1671-9352.0.2022.058 |
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| Authors: | ZHANG Wei GUO Ji-dong ZHANG Liang |
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| Affiliation: | 1. College of Mathematics and Statistics;2. Institute of Applied Mathematics, Yili Normal University, Yining 835000, Xinjiang, China |
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| Abstract: | Based on the group structure and the order of elements of a class of non-abelian groups in group theory, the number of endomorphisms and automorphisms of a class of non-abelian groups of order 2qpn whose Sylow p-subgroups is cyclic is calculated, where qand both are odd primes. Moreover, it is proved that the number of endomorphisms of such groups satisfies the conjecture of T. Asai and T. Yoshida in this case. |
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| Keywords: | non-abelian group endomorphism automorphism conjecture of T.Asai & T.Yoshida |
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