AN EXPLICIT FORMULA FOR THE NUMBER OF DISTINCT FUZZY SUBGROUPS OF THE CARTESIAN PRODUCT OF THE DIHEDRAL GROUP OF ORDER 2n WITH A CYCLIC GROUP OF ORDER 2

The Generalized Quarternion p-Group of Order 2n : Discovering the Fuzzy Subgroups

“…Following our paper [1](Also see [2] and [5]) the following equation(#) based on the usual Inclusive-Exclusive technique is appliied :…”

The Explicit Formula for the Number of the Distinct Fuzzy Subgroups of the Cartesian Product of the Dihedral Group 2n with a Cyclic Group of Order Eight , where n > 3

“…Theorem 2.1. [2] Let ‫ܩ‬ = ‫ܦ‬ ଶ × ℂ ଶ , the nilpotent group formed by the cartesian product of the dihedral group of order 2 and a cyclic group of order 2. Then, the number of distinct fuzzy subgroups of ‫ܩ‬ is given by : ℎ(‫)ܩ‬ = 2 ଶ (2݊ + 1) − 2 ାଵ , ݊ > .3…”

2-Dimensional Subgroups of the Quasidihedral Group of Order 2n with a Cyclic Group of Order 2

“…are the maximal subgroups of G The method of computing ) (G h is based on the application of the Inclusion-Exclusion Principle. This had been extensively discussed in our article [1] Following our paper [1] the following equation(*) based on the usual Inclusive-Exclusive technique is appliied :…”