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.

MSC (2010): Primary 20N25, 03E72; Secondary 05E15, 20D30, 20D60.

Keywords: Fuzzy subgroups, chains of subgroups, maximal chains of subgroups, symmetric groups, recurrence relations.

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