  The purpose of the present paper is to consider the notion of isoclinism
between two finite groups and its generalization to n-isoclinism, introduced by
J. C. Bioch in 1976. A weaker form of n-isoclinism, called relative
n-isoclinism, will be discussed. This will allow us to improve some classical
results in literature. We will point out the connections between a relative
n-isoclinism and the notions of commutativity degree, n-th nilpotency degree
and relative n-th nilpotency degree, which arouse interest in the
classification of groups of prime power order in the last years.
