An extension of commutativity degree of finite groups

Document Type : Research Paper

Author

Faculty of mathematical sciences, University of Guilan

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

Journal of Algebra and Related Topics

Articles in Press, Accepted Manuscript
Available Online from 04 December 2024

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