Commutativity Degrees of Wreath Products of Finite Abellian Groups
Igor V. Erovenko · NC Digital Online Collection of Knowledge and Scholarship (The University of North Carolina at Greensboro) · 2008
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.