The structure of ν-isologic pairs of groups

Abstract

In [2], the first two authors generalized the concept of n-isoclinism to the class of all pairs of groups. In this paper, we extend that notion to ν-isologism and study the details of this notion. In addition, it is shown that every pair of groups is ν-isologic with a quotient irreducible pair of groups. Finally, as an application, we drive some inequalities for the Baer-invariant of a pair of groups.