Combinatorics of counting distinct fuzzy subgroups of certain dihedral group

Abstract

This paper is devoted to counting distinct fuzzy subgroups (DFS) of finite dihedral group D2n, where n is a product of finite number of distinct primes, with respect to the equivalence relation ≈ . This counting has connections with familiar integer sequence called ordered Bell numbers. Furthermore, a recurrence relation and generating function was derived for counting DFS of D2n.