On fuzzy subgroups of finite p-groups
by
hossein Naraghi
Tarbiat Modares University
Coauthors: Hassan Naraghi and Ali Iranmanesh

The general problem of classification of fuzzy subgroups of a finite group of any given order is both important and interesting. Recently, some authors have used the equivalence relations on fuzzy subgroups to study the equivalent of fuzzy subgroups [1-3].
Let F₁(G) be the set of all fuzzy subgroups m of G such that m(e)=1. In this paper, we will define a new relation on F₁(G) and obtain a connection between this relation and other relations which defined in the above papers.
In group theory, one of the main work is the probability of two elements of a group and many paper published in this area. A natural question is arise: is it possible bring this concept in fuzzy groups and obtain the same results in group theory. Since one of the important and interesting groups in finite groups and fuzzy groups is the cyclic group Z_pⁿ , we focus on this group. In this paper we define the probability of counting two fuzzy subgroups of Z_pⁿ and by the above results, we obtain some interesting results on this group and give more information about the structure of these groups in the combine of fuzzy subgroups with group theory.
References.
1. C. Degang and J. Jiashang, Some notes on equivalence fuzzy sets and fuzzy subgroups, Fuzzy Sets and Systems, 152(2005)403-409.
2. Marius T\checkarn\checkauceanu and Lucian Bentea, On the number of fuzzy subgroups of finite abelian groups, to appear in Fuzzy Sets and Systems.
3. V. Murali and B. B. Makamba, Counting the number of fuzzy subgroups of an abelian group of order pⁿq^m, Fuzzy Sets and Systems, 144(2004)459-470.

Date received: February 14, 2008