| 一类非交换内循环群到有限群的同态个数 |
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| 引用本文： | 张良.一类非交换内循环群到有限群的同态个数[J].吉林大学学报(理学版),2020,58(6):1299-1302. |
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| 作者姓名： | 张良 |
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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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| 基金项目： | 新疆维吾尔自治区高校科研计划项目;伊犁师范大学博士科研启动基金 |
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| 摘 要： | 首先, 利用群论和同余理论计算一类非交换内循环群的自同态个数和自同构个数, 并给出该类内循环群到一般有限群同态个数满足的数量关系; 其次, 验证上述情形的数量关系对Asai和Yoshida猜想成立.
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| 关 键 词： | 内循环群 群同态 自同态 自同构 |
Number of Homomorphisms from a Class of Non Commutative Inner Cyclic Groups to Finite Groups |
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| ZHANG Liang.Number of Homomorphisms from a Class of Non Commutative Inner Cyclic Groups to Finite Groups[J].Journal of Jilin University: Sci Ed,2020,58(6):1299-1302. |
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| Authors: | ZHANG Liang |
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| Institution: | College of Mathematics and Statistics, Yili Normal University, Yining 835000, Xinjiang Uygur Autonomous Region, China |
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| Abstract: | Firstly, by using group theory and congruence theory, the author calculated the number of endomorphisms and automorphisms between a class of non commutative inner cyclic groups, and gave the quantity relation of the number of homomorphisms from such inner cyclic groups to finite groups. Secondly, the author verified that the conjectures of Asai and Yoshida were true for the above cases. |
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| Keywords: | inner cyclic groups homomorphism endomorphism automorphism |
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