What is the probability that two elements of a finite group commute?

Commuting probability for subrings and quotient rings

“…There has been much written on the commuting probability of a finite group: see for instance [5], [7], [8], [10], [4], and [6]. The commuting probability of a ring has been discussed in [9], [3], [2], and [1].…”

Multiplicative degree of some dihedral groups

“…The commutativity degree of a group G is the probability that a selected chosen pair of elements of a group G commute, denoted by P(G), and it was firstly introduced by Miller [1] in 1944. The commutativity degree has been investigated by several authors [2][3][4][5][6] and some formulas of P(G) have been found for some finite groups G.…”

Finite Rings with Large Anticommuting Probability

“…There has been much written on the possible values attained by the probability that a random pair of elements in a finite group commute: see for instance [5], [9], [7], [10], [12], [4], [6], [3], and [8]. The corresponding question for finite rings was examined in [11] and [2].…”