Author/Authors :
Pourmirzaei، Azam نويسنده Department of Mathematics, Hakim Sabzevari University, P.O.Box 96179-76487, Sabzevar, Iran. , , Hassanzadeh، Mitra نويسنده Department of Mathematics, Department of Mathematics, Ferdowsi University of Mashhad, P.O.Box 1159-91775, Mashhad, Iran. , , Mashayekhy، Behrooz نويسنده Department of Pure Mathematics, Center of Excellence in Analysis on Algebraic Structures, ,
Abstract :
Abstract. Let (G;N) be a pair of groups. In this paper, rstly,
we construct a relative central extension for the pair (G;N) such
that special types of the covering pair of (G;N) are the homomor-
phic image of it. Secondly, we show that every perfect pair admits
at least one covering pair. Finally, among extending some proper-
ties of perfect groups to perfect pairs, we characterize the covering
pairs of a perfect pair (G;N) under some extra assumptions.
