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 ?-isologism and study the details of this notion. In addition, it is shown that every pair of groups is ?-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.
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