An extension of commutativity degree of finite groups

Document Type : Research Paper

Authors

1 Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran

2 Department of Mathematics, University Campus 2, University of Guilan, Rasht, Iran

Abstract

Let G be a finite group. The commutativity degree of G, written d(G), is defined as the ratio
|{(x, y)|x, y \in G, xy = yx}|/|G|^2. In this paper, we first extend this concept of finite groups to the
commutativity degree of fuzzy subgroups. Then, by using the numerical solutions of the equation xy − zu \eqiv t(mod n), we give explicit formulas for the commutativity degree of fuzzy subgroups of 2-generated groups of nilpotency class 2. Finally we show that this method also works for a large class of finite groups, including
metabelian groups.

Keywords

References

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Journal of Algebra and Related Topics
Volume 13, Issue 2
December 2025
Pages 15-26

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