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.
By using the equivalence class of group action,the set of cocycles and the group homomorphism were connected.By characterizing the 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 the set 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 G could be divided by the greatest common divisor of ∣A∣and∣G∣.
作者
李青凤
海进科
LI Qingfeng;HAI Jinke(School of Mathematics and Statistics,Qingdao University,Qingdao266071,Shandong Province,China)
出处
《吉林大学学报（理学版）》
CAS
北大核心
2019年第1期32-36,共5页
Journal of Jilin University:Science Edition
基金
山东省自然科学基金(批准号:ZR2016AM21)
关键词
上循环
群作用
群同态
有限群
cocycle
group action
homomorphism
finite group
