| 有限可解群的Fuzzy子群的阶数及其等价类数 |
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| 引用本文： | 宋明娟,赵国亮,黄沙日娜.有限可解群的Fuzzy子群的阶数及其等价类数[J].模糊系统与数学,2009,23(3). |
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| 作者姓名： | 宋明娟 赵国亮 黄沙日娜 |
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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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| 基金项目： | 黑龙江省教育厅科研项目，黑龙江科技学院引进高层次人才科研启动基金资助项目 |
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| 摘 要： | 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.
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| 关 键 词： | 有限可解群 水平集的阶 等价关系 极大F子群 F子群 因数列 商数列 极大因数列 |
On the Number of Equivalent Classes of Fuzzy Subgroups of a Finite Solvable Group |
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| SONG Ming-juan,ZHAO Guo-liang,HUANG Sha-ri-na.On the Number of Equivalent Classes of Fuzzy Subgroups of a Finite Solvable Group[J].Fuzzy Systems and Mathematics,2009,23(3). |
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| Authors: | SONG Ming-juan ZHAO Guo-liang HUANG Sha-ri-na |
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| Institution: | Department of Mathmatics and Mechanics;Heilongjiang Institute of Science and Technology;Harbin 150027;China |
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| Abstract: | 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... |
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| Keywords: | Finite Solvable Group The Order of a Level Set Equivalent Relationship Maximal Fuzzy Subgroup Quotient Series of a Group Quotient Series of a Number Maximal Divisor Series of a Number |
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