A Recursive Formula for the Number of FuzzySubgroups of Finite Cyclic Groups

Subject Areas : B. Computer Systems Organization

Mahdi Imanparast ¹ , Hamid Darabi ²

1 - Department of Computer Science, University of Bojnord, Bojnord, Iran
2 - Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran

Received: 2013-08-28 Accepted : 2013-08-28 Published : 2013-01-01

Keywords: Fuzzy groups, Lattice, Finite cyclic groups, Chains,

Abstract :

Fuzzy groups and fuzzy theory have a lot of applications in several sciences such as mathematics, computer science, computer and electrical engineering. Hence, counting the number of fuzzy subgroups of finite groups to classify them is an important issue in fuzzy theory. The Main goal of this paper is to give an explicit formula for the number of fuzzy subgroups of a finite cyclic group G Z p1 Z p 2 Z p 3 Z pk = ´ ´ ´´ , where k p , p ,..., p 1 2 are distinct prime numbers. We introduce a very simple recursive formula to count the number of subgroups of G.