Strong restrictions on the structure of a group $G$ can be given, once that itis known the probability that a randomly chosen pair of elements of a finitegroup $G$ commutes. Introducing the notion of mutually commuting n-tuplesfor compact groups (not necessary finite), the present paper generalizes theprobability that a randomly chosen pair of elements of $G$ commutes. We shallstate some results concerning this new concept of probability which has beenrecently treated in . Furthermore a relation has been found between thenotion of mutually commuting n-tuples and that of isoclinism between twoarbitrary groups.
|Numero di pagine||10|
|Rivista||ITALIAN JOURNAL OF PURE AND APPLIED MATHEMATICS|
|Stato di pubblicazione||Published - 2009|