M. R. R. Moghaddam, A. R. Salemkar and A.Gholami

Abstract
Let $\Cal V$ be a variety of groups defined by the set of laws $V$. In this paper, we give a necessary and sufficient condition for a marginal extension to be irreducible and primitive, with respect to a given variety $\Cal V$. It is also shown the existence of $\Cal V$-marginal irreducible extension and a $\Cal V$-covering group of a given $\Cal V$-perfect group.