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

TL;DR

This paper derives formulas for counting fuzzy subgroups in finite abelian groups of order p^n q^m, providing explicit counts for specific group structures.

Contribution

It introduces explicit formulas for the number of fuzzy subgroups in finite abelian groups of order p^n q^m, expanding understanding of fuzzy subgroup enumeration.

Findings

Formulas for fuzzy subgroups of groups of order p^n q^m

Explicit counts for groups like Z_p^n x Z_q^m and Z_{p^n} x Z_q^m

Enhanced methods for fuzzy subgroup enumeration in finite abelian groups

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.