Some Functorial Properties of Nilpotent Multipliers

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In this paper, we are going to look at the c-nilpotent multiplier of a group G, NcM(G), as a functor from the category of all groups, Group, to the category of all abelian groups, Ab, and focusing on some functional properties of it. In fact, by using some results of the first author and others and finding an explicit formula for the c-nilpotent multiplier of a finitely generated abelian group, we try to concentrate on the commutativity of the above functor with the two famous functors Ext and Tor.