On the Subgroups Lattice and Fuzzy Subgroups of Finite Groups U6n

Abstract

In this paper, we treat accounting for the number of fuzzy (normal) subgroups of finite groups [Formula: see text]. In order to do this, we use the natural equivalence relation on the set of fuzzy (normal) subgroups of [Formula: see text], which has a consistent group theoretical foundation. In fact, the corresponding equivalence classes of fuzzy (normal) subgroups of [Formula: see text] are closely connected to the structure of (normal) subgroups lattice of [Formula: see text] and chains of subgroups of [Formula: see text], which terminate in [Formula: see text]. 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.

Keywords

• Equivalence relation
• lattice
• fuzzy subgroup
• chain of subgroups
• level subset
• metacyclic group