计算模糊子群的等价类

计算模糊子群的等价类 Counting the Number of the Equivalent Classes for Fuzzy Groups 詹环 ZHAN Huan 1 2 first-author 黄本文 HUANG Ben-wen 1 2 李圣国 LI Sheng-guo 1 2 胡文超 HU Wen-chao 1 2 武汉大学数学与统计学院 武汉大学数学与统计学院 School of Mathematics and Statistics,Wuhan University School of Mathematics and Statistics,Wuhan University 武汉大学数学与统计学院,湖北,武汉,430072 武汉大学数学与统计学院,湖北,武汉,430072 在群同构意义下即可对经典子群进行等价分类.模糊子群是对经典子群的推广,将模糊子群用一系列水平子群形成的极大子群链来描述,由群的格可得极大子群链,模糊子群的分类就转化为极大水平子群链的等价分类.从子群的格的角度出发,得到了有限群的模糊子群等价类个数的具体范围.计算出阶为pq的有限群的模糊子群的等价类个数. Groups are equivalent if and only if they are isomorphic.Fuzzy group is a generalization of crisp group.Fuzzy groups are chains of crisp groups formed by maximal-level subgroups.The classification of fuzzy subgroups rests mainly on the lattice of subgroups from which maximal-level subgroups chains can be obtained.Thus,to find distinct fuzzy subgroups we only need to present distinct maximal-level subgroups chains.In this way,we determine the range of equivalent classes of fuzzy subgroups of a finite group.In particular,we propose distinct equivalence classes of fuzzy subgroups of a group of order pq. 有限群 等价类 模糊子群 水平子群 finite group equivalent classes fuzzy group level subgroup O159 湖北省自然科学基金资助项目（99J165） 2005-01-01 2021-04-01 S2