Shahrood University of Technology Journal of Algebraic Systems 2345-5128 4 1 2016 09 01 ON RELATIVE CENTRAL EXTENSIONS AND COVERING PAIRS 1 13 724 10.22044/jas.2016.724 EN A. Pourmirzaei Department of Mathematics, Hakim Sabzevari University, P. O. Box 96179-76487, Sabzevar, Iran M. Hassanzadeh Department of Mathematics, Department of Mathematics, Ferdowsi University of Mashhad, P.O.Box 1159-91775, Mashhad, Iran. B. Mashayekhy Department of Mathematics, Center of Excellence in Analysis on Algebraic Struc- tures, Ferdowsi University of Mashhad, P.O.Box 1159-91775, Mashhad, Iran. Journal Article 2015 03 02 Let (G;N) be a pair of groups. In this article, first we con-<br />struct a relative central extension for the pair (G;N) such that special<br />types of covering pair of (G;N) are homomorphic image of it. Second, we<br />show that every perfect pair admits at least one covering pair. Finally,<br />among extending some properties of perfect groups to perfect pairs, we<br />characterize covering pairs of a perfect pair (G;N) under some extra<br />assumptions. https://jas.shahroodut.ac.ir/article_724_70e8def60b0539607f4789672c9b8d32.pdf