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

Relative n-isoclinism classes and relative n-th nilpotency degree of finite groups