Abstract Let $F_{\\infty}$ be a free group on a countable set $\\{ x_1,x_2,\\cdots \\}$ and ${\\cal V}$ be a variety of groups, defined by the set of laws $V$, in the free generators $x_i$\'s. In this talk our aim is to exhibit some close relationships between the groups ${\\cal V}M(G)$ and ${\\cal V}M(G/N)$, where $N$ is a normal subgroup contained in the marginal subgroup of $G$ with respect to the variety $\\cal V$. Using these relationships we shall give a necessary and sufficient condition for a group $G$ to be $\\cal V$-capable.

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