有限循环群的Fuzzy子群的等价类数

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

有限循环群 G的 F子群可以有无数个 ,但是 ,若当两个 F子群的水平集构成的集合相等就称其等价的话 ,那么其等价类数是有限的。通过研究群的合成群列、商群列以及数的因数列和极大因数列找出了有限循环群的极大 F子群和 F子群的等价类数的求解公式 。

A finite Cycle group has infinite fuzzy subgroups. But these fuzzy subgroups' the number of equivalent classes is finite, if two fuzzy subgroups are called as equivalence when the set consists of the order of the level sets of the one fuzzy subgroup is equal with the another's .In this paper, by means of studying the composition series and the quotient series of a group as well as the divisor series and the maximal divisor series of a number, obtain the formulas to find the number of equivalent classes of maximal fuzzy subgroups and fuzzy groups of a Cycle group, and have found the relationship formula on them.