涉及多重和的Fuzzy子群结果
The fuzzy subgroups results involving multiple sums
摘要：
模糊集理论有着广泛的应用，模糊群就是其中之一。模糊集是由Zadeh提出的。尽管模糊逻辑的故事开始得更早，但它在数学上是专门设计来表示不确定性和不确定性的。它也是为了提供正式的工具来处理许多问题所固有的不精确性。一个群称为幂零群，如果它有一个有限长n的正规列。根据这个概念，每个有限p-群都是幂零的。幂零结构，如p-群，具有有限长度的正规列。任何有限p-群都有许多正规子群，因而存在大量给定阶的非同构子群的现象。这使得它成为组合和上同调研究的理想对象。笛卡儿积（又称积集）在抽象群的综合过程中起着至关重要的作用。以前的研究已经确定了各种有限p-群的不同模糊子群的数量，包括那些平方自由阶。然而，对于p-群的笛卡儿积所构成的幂零群，通过计算得到的模糊子群分类却没有做太多的工作。因此，本文通过计算p-群的笛卡儿积所形成的幂零群来对它们进行分类.利用p-群的笛卡儿积得到了幂零群.给出了8阶二面体群与2的n次幂的循环群的笛卡儿积的不同Fuzzy子群个数的显式表达式，其中n不小于小于3
英文摘要：
The theory of fuzzy sets has a wide range of applications, one of which is that of fuzzy groups . The fuzzy sets were introduced by Zadeh. Even though, the story of fuzzy logic started much earlier, it was specially designed mathematically to represent uncertainty and vagueness. It was also, to provide formalized tools for dealing with the imprecision intrinsic to many problems. A group is said to be nilpotent if it has a normal series of a finite length n. By this notion, every finite p-group is nilpotent. Nilpotent structures such as the p-groups, have normal series of finite length. Any finite p-group has many normal subgroups and consequently, the phenomenon of large number of non-isomorphic subgroups of a given order. This makes it an ideal object for combinatorial and cohomological investigations. Cartesian product (otherwise known as the product set) plays vital roles in the course of synthesizing the abstract groups. Previous studies have determined the number of distinct fuzzy subgroups of various finite p-groups including those of square-free order. However, not much work has been done on the fuzzy subgroup classification for the nilpotent groups formed from the Cartesian products of p-groups through their computations. This work is therefore designed to classify the nilpotent groups formed from the Cartesian products of p-groups through their computations. In this paper, the Cartesian products of p-groups were taken to obtain nilpotent groups. the explicit formulae is given for the number of distinct fuzzy subgroups of the Cartesian product of the dihedral group of order eight with a cyclic group of order of an n power of two for, which n is not less than three
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