ScholarLens Back to search
2008•NC Digital Online Collection of Knowledge and Scholarship (The University of North Carolina at Greensboro)Open access

Commutativity Degrees of Wreath Products of Finite Abellian Groups

Igor V. Erovenko

Open full text 0 citations

Abstract

We compute commutativity degrees of wreath products AoB of finite abelian groups A and B. When B is fixed of order n the asymptotic commutativity degree of such wreath products is 1=n2. This answers a generalized version of a question posed by P. Lescot. As byproducts of our formula we compute the number of conjugacy classes in such wreath products, and obtain an interesting elementary number-theoretic result.

Open-access reader

About this research paper

What this paper is about

We compute commutativity degrees of wreath products AoB of finite abelian groups A and B. When B is fixed of order n the asymptotic commutativity degree of such wreath products is 1=n2. This answers a generalized version of a question posed by P. Lescot. As byproducts of our formula we compute the number of conjugacy classes in such wreath products, and obtain an interesting elementary number-theoretic result.

Why it matters

A significance statement is not available in the OpenAlex record.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

We compute commutativity degrees of wreath products AoB of finite abelian groups A and B. When B is fixed of order n the asymptotic commutativity degree of such wreath products is 1=n2. This answers a generalized version of a question posed by P. Lescot. As byproducts of our formula we compute the number of conjugacy classes in such wreath products, and obtain an interesting elementary number-theoretic result.

Key concepts: Wreath product, Mathematics, Conjugacy class, Commutative property, Abelian group, Pure mathematics, Finite group, Group (periodic table)

Related papers

Related paper 1Related paper 2Related paper 3
Back to paper searchBrowse research topicsOriginal source
Commutativity Degrees of Wreath Products of Finite Abellian Groups — Research Paper | ScholarLens