| 群同态个数的刻画 |
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| 引用本文： | 李青凤,海进科. 群同态个数的刻画[J]. 吉林大学学报(理学版), 2019, 57(1): 32-36 |
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| 作者姓名： | 李青凤 海进科 |
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| 作者单位： | 青岛大学数学与统计学院,山东青岛,266071;青岛大学数学与统计学院,山东青岛,266071 |
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| 摘 要： | 利用群作用的等价类, 将上循环集与群同态进行联系. 通过上循环集对两个有限群之间的同态个数进行刻画, 证明了对任意有限群A,G, 如果A,G的上循环集中元素的个数可被|A|和|G|的最大公因子整除, 则A,G之间的同态个数可被|A|和|G|的最大公因子整除.
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| 关 键 词： | 上循环 群作用 群同态 有限群 |
| 收稿时间： | 2018-01-22 |
Characterization of Number of Group Homomorphisms |
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| LI Qingfeng,HAI Jinke. Characterization of Number of Group Homomorphisms[J]. Journal of Jilin University: Sci Ed, 2019, 57(1): 32-36 |
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| Authors: | LI Qingfeng HAI Jinke |
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| Affiliation: | School of Mathematics and Statistics, Qingdao University, Qingdao 266071, Shandong Province, China
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| Abstract: | By using the equivalence class of group action, the set of cocycles and the group homomorphism were connected. By characterizingthe number of homomorphisms between two finite groups through the set of cocycles, we proved that for any finite groups A,G, if the number of elements in theset of cocycles of A and G could be divided by the greatest common divisor of |A| and |G|, the number of homomorphisms between A and Gcould be divided by the greatest common divisor of |A| and |G|. |
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| Keywords: | cocycle group action homomorphism finite group |
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