Document Type : Research Paper
Department of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran.
Department of Mathematics, Quchan University of Technology, Quchan, Iran.
Let G be a finite group. The notion of n-Engel degree of G, denote by dn(G), is the probability of two randomely chosen elements x, y ∈ G satisfy the n-Engel condition [y,n x]=1. The case n=1 is the known commutativity degree of G. The aim of this paper, is to define and investigate the relative 2-Engel degree of a subgroup H of G as the probability of two randomely chosen elements x∈G and y∈H satisfy the 2-Engel condition [y,2 x]=1.