Classifying Fuzzy Subgroups of Dicyclic Groups
B. Davvaz and L. Kamali Ardekani
The dicyclic group T4n, also called the binary dihedral group with parameter n > 1, is a subgroup of the unit quaternions generated by x = e iπ /n and y = j. In this paper, we consider the natural equivalence relation introduced by Tarnauceanu and we determine the number of fuzzy subgroups of dicyclic groups. Explicit formulas are obtained in the particular cases of dicyclic groups. An essential role in solving our counting problem will be played by the Inclusion-Exclusion Principle.
Keywords: Fuzzy subgroups, chains of subgroups, dicyclic group, supersolvable, recurrence relations.
MSC: 20N25, 03E72, 05E15