Let F_{ infty} be a free group on a countable set { x_1,x_2, cdots } and { cal V} be a variety of group, defined by the set of outer commutators V , in the free generators x_i s. The paper is devoted to give the complete structure of a { cal V} -covering of { cal V} -perfect groups. Furthermore a necessary and sufficient conditions for the universality of a { cal V} -central extension by a group and its { cal V} -covering group will be presented.

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