On the converse of Fuzzy Lagrange's Theorem

TL;DR

This paper explores the converse of a fuzzy group theory version of Lagrange's theorem, providing a characterization of finite cyclic groups through this perspective.

Contribution

It introduces a new characterization of finite cyclic groups by analyzing the converse of a fuzzy Lagrange's theorem.

Findings

Characterization of finite cyclic groups via fuzzy Lagrange's theorem

Insight into the structure of fuzzy groups related to classical group theory

Extension of Lagrange's theorem concepts to fuzzy group contexts

Abstract

In fuzzy group theory many versions of the well-known Lagrange's theorem have been studied. The aim of this article is to investigate the converse of one of those results. This leads to an interesting characterization of finite cyclic groups.