基于模糊超群构建的Engel群及其性质研究

Research on Engel groups based on fuzzy hypergroupsand their properties

通过构造满足Engel递减条件的模糊超群(H,。)上最小的等价关系■^(*),使得模糊超群关于等价关系构建的商群(等价类的集合)H/■^(*)是一个Engel群,并通过等价关系的强正则性来刻画该Engel群,最后引入模糊超群的?-部分的概念,确定等价关系?是可传递的充要条件.

By constructing the smallest equivalence relation ■^(*) on a fuzzy hypergroup(H,)satisfying the Engel decreasing condition,the quotient group(the set of equivalence classes)H/■^(*) constructed by the fuzzy hypergroup with respect to the equivalence relation is an Engel group,and the Engel group is characterized by the strong regularity of the equivalence relation.Finally,the concept of the-part of the fuzzy hypergroup is introduced,and the necessary and sufficient condition for the equivalence relation to be transitive is determined.