Let $\\cal V$ be a variety of groups defined by the set of laws $V$. In this paper, we will show that every group $G$ possesses a uniquely determined subgroup $(V^*)^*(G)$ of marginal subgroup $V^*(G)$ , which is minimal subject to being the image in $G$ of the marginal subgroup of some $\\cal V$-marginal extension of $G$. $(V^*)^*(G)$ is characteristic and is also the smallest subgroup of $V^*(G)$ whose factor-group is $\\cal V$-capable. Hence a necessary and sufficient condition for ${\\cal V}$-capability will be presented. Furthermore, it will be shown that the class of all ${\\cal V}$-capable groups is closed under the direct products.

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