On the Subgroups Lattice and Fuzzy Subgroups of Finite Groups U 6n

Abstract

In this paper, we treat accounting for the number of fuzzy (normal) subgroups of finite groups . In order to do this, we use the natural equivalence relation on the set of fuzzy (normal) subgroups of , which has a consistent group theoretical foundation. In fact, the corresponding equivalence classes of fuzzy (normal) subgroups of are closely connected to the structure of (normal) subgroups lattice of and chains of subgroups of , which terminate in . In this regards, the Inclusion-Exclusion principle plays an essential role and in some situations leads to recurrence relations, whose their solutions can be easily found.