Given a finitely generated nilpotent group $\mathcal{N}$, let $\mathcal{N}=\mathcal{N}_{0}\rhd\mathcal{N}_{1}\rhd\ldots\rhd\mathcal{N}_{m}=\{e\}$ be the lower central series with abelian factor groups $\mathcal{N}_{j-1}/\mathcal{N}_{j}$, where $\mathcal{N}_{j+1}\equiv[\mathcal{N},\mathcal{N}_{j}]$ are the commutator subgroups. Then the nilpotent rank of $\mathcal{N}$ is defined as the sum of the ranks of the abelian factors, i.e.