Strong restrictions on the structure of a group $G$ can be given, once that it is known the probability that a randomly chosen pair of elements of a finite group $G$ commutes. Introducing the notion of mutually commuting n-tuples for compact groups (not necessary finite), the present paper generalizes the probability that a randomly chosen pair of elements of $G$ commutes. We shall state some results concerning this new concept of probability which has been recently treated in . Furthermore a relation has been found between the notion of mutually commuting n-tuples and that of isoclinism between two arbitrary groups.
Erfanian, A., Russo, F. (2009). Isoclinism in probability of commuting n-tuples. ITALIAN JOURNAL OF PURE AND APPLIED MATHEMATICS, 25, 27-36.