Commutativity degrees of wreath products of finite Abelian groups

Abstract

We compute commutativity degrees of wreath products A wreath product B 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. © 2008 Australian Mathematical Society.