有限可解群的Fuzzy子群的阶数及其等价类数

On the Number of Equivalent Classes of Fuzzy Subgroups of a Finite Solvable Group

定义Fuzzy子群的一种等价关系,即:如果两个Fuzzy子群的水平集的阶构成的集合相等,就称这两个Fuzzy子群等价,并且通过研究群的子群列以及群阶的因数列和商数列找出了有限可解群的极大Fuzzy子群和Fuzzy子群的阶和等价类数的求解公式,并给出了二者之间的关系式。

In this paper, we define an equivalent relationship on fuzzy subgroups. That is, if the set consisting of the order of the level sets of fuzzy subgroup is equal with the others , they are equivalent. By means of studying the composition series and the quotient series of a group as well as the divisor series and the quotient series of a number, we obtain the formulas to find the number of equivalent classes of maximal fuzzy subgroups and fuzzy groups of a finite solvable group, and have established the relationship between them.