On the Number of Fuzzy Subgroups of Finite Symmetric Groups
Marius Tarnauceanu
The main goal of this paper is to classify the fuzzy subgroups of the finite symmetric group Sn. Explicit formulas for the number of distinct fuzzy subgroups of Sn are obtained in the particular cases n = 3 and n = 4. Some inequalities satisfied by this number are also established for n ≥ 5.
Keywords: Fuzzy subgroups, chains of subgroups, maximal chains of subgroups, symmetric groups, recurrence relations.
MSC (2010): Primary 20N25, 03E72; Secondary 05E15, 20D30, 20D60.