Nilpotent multiplier

Definition
Suppose $$c$$ is a positive integer. The $$c$$-nilpotent multiplier of a group $$G$$, denoted $$M^{(c)}(G)$$ is defined as the defining ingredient::Baer invariant of $$G$$ with respect to the variety of groups of nilpotency class (at most) $$c$$. If we write $$G = F/R$$ where $$F$$ is a free group, this can be written as:

$$M^{(c)}(G) = \frac{R \cap \gamma_{c+1}(F)}{[[\dots[R,F],\dots,F],F]}$$

where $$\gamma_{c+1}(F)$$ denotes the $$(c+1)^{th}$$ member of the lower central series of $$F$$ and the denominator group has $$c$$ occurrences of $$F$$.

Particular cases
In the case $$c = 1$$, we get the Schur multiplier.