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The first author, in 2001, presented a structure for the Baer-invariant of anilpotent product of cyclic groups with respect to the variety of nilpotentgroups. In this paper, using the above structure, we prove the existence of an${\cal N}_c$-covering group for a nilpotent product of a family of cyclicgroups. We also present a structure for the ${\cal N}_c$-covering group.

On ${\cal N}_c$-Covering Groups of a Nilpotent Product of Cyclic Groups