We compute commutativity degrees of wreath products A o 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 numbe...

In this article we introduce and study the concept of characteristic degree of a subgroup in a finite group. We define the characteristic degree of a subgroup H in a finite group G as the ratio of the number of all pairs (h,α) ∈ H×Aut(G) such that h^α∈H, by the order of H × Aut(G), where Aut(G) is the automorphisms group of G. This quantity measures the probability that H can be characteristic ...

For a given element $g$ of finite group $G$, the probablility that commutator randomly choosen pair elements in $G$ equals is relative commutativity degree $g$. In this paper we are interested studying Dihedral order $2n$ and Quaternion $2^{n}$ for any $n\geq 3$ examine infinite class Moufang Loops Chein type, $M(G,2)$.