Abstract
The purpose of this paper is to give a relation between the notion of the commutativity degree of a finite group G (denoted by d(G)) and that of isoclinism between G and an extra special p-group, where p is the smallest prime number dividing |G|. Moreover, some improvements of the results on the relative commutativity degree and relative n th nilpotency degree of a subgroup of finite groups given in [A. Erfanian, R. Rezaei and P. Lescot, On the relative commutativity degree of a subgroup of a finite group, Comm. Algebra35 (2007) 4183–4197] are also stated in this paper.
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