The number of fuzzy subgroups of a finite abelian group of order $p^n{q}^m$

Abstract

The purpose of this paper is to determine the number of fuzzy subgroups of a finite abelian group of order $p^n{q}^m$. As an application of our main result, explicit formulas for the number of fuzzy subgroups of ${\mathbb{Z}}_p^n\times {\mathbb{Z}}_q^m$ and ${\mathbb{Z}}_{p^n}\times {\mathbb{Z}}_q^m$ are given.

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