In mathematics and more precisely in group theory, the commuting probability (also called degree of commutativity or commutativity degree) of a finite group is the probability that two randomly chosen elements commute.
[1][2] It can be used to measure how close to abelian a finite group is.
It can be generalized to infinite groups equipped with a suitable probability measure,[3] and can also be generalized to other algebraic structures such as rings.
as the averaged number of pairs of elements of
denotes the cardinality of a finite set
is the probability that two randomly chosen elements of
is called the commuting probability of