Nilpotent Group

A Group $G$ for which the chain of groups

$$I=Z_0\subseteq Z_1\subseteq \ldots \subseteq Z_n$$

with $Z_{k+1}/Z_k$ (equal to the Center of $G/Z_k$) terminates finitely with $G=Z_n$ is called a nilpotent group.

See also Center (Group), Nilpotent Lie Group