A. Pourmirzaei - Department of Mathematics, Hakim Sabzevari University, P. O. Box ۹۶۱۷۹-۷۶۴۸۷, Sabzevar, Iran
M. Hassanzadeh - Department of Mathematics, Department of Mathematics, Ferdowsi University of Mashhad, P.O.Box ۱۱۵۹-۹۱۷۷۵, Mashhad, Iran.
B. Mashayekhy - Department of Mathematics, Center of Excellence in Analysis on Algebraic Struc- tures, Ferdowsi University of Mashhad, P.O.Box ۱۱۵۹-۹۱۷۷۵, Mashhad, Iran.

Let (G;N) be a pair of groups. In this article, first we con-struct a relative central extension for the pair (G;N) such that specialtypes of covering pair of (G;N) are homomorphic image of it. Second, weshow that every perfect pair admits at least one covering pair. Finally,among extending some properties of perfect groups to perfect pairs, wecharacterize covering pairs of a perfect pair (G;N) under some extraassumptions.

Pair of groups, Covering pair, Relative central extension, Isoclinism of pairs of groups