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 [3]. Furthermore a relation has been found between the notion of mutually commuting n-tuples and that of isoclinism between two arbitrary groups.

Keywords