| 有限循环群的Fuzzy子群的等价类数 |
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| 引用本文： | 宋明娟. 有限循环群的Fuzzy子群的等价类数[J]. 模糊系统与数学, 2003, 17(3): 77-79 |
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| 作者姓名： | 宋明娟 |
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| 作者单位： | 黑龙江科技学院,数力系,黑龙江,哈尔滨,150027 |
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| 摘 要： | 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．并给出二者之间的关系式．
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| 关 键 词： | 等价类 极大F子群 合成群列 商群列 因数列 极大因数列 |
| 文章编号： | 1001-7402(2003)03-0077-03 |
| 修稿时间： | 2002-06-13 |
On the Number of Equivalent Classes of Fuzzy Subgroups of a Finite Cycle Group |
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| SONG Ming juan. On the Number of Equivalent Classes of Fuzzy Subgroups of a Finite Cycle Group[J]. Fuzzy Systems and Mathematics, 2003, 17(3): 77-79 |
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| Authors: | SONG Ming juan |
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| Abstract: | 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. |
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| Keywords: | Equivalent Class Maximal Fuzzy Subgroup Composition Series of a Group Quotient Series of a Group Divisor Series of a Number Maximal Divisor Series of a Number |
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