Abstract Algebra
《Abstract Algebra》 · 第 190 页 · Section 6.1「$p$-groups, Nilpotent Groups, and Solvable Groups」，Definition
For any group $G$, define $Z_0(G)=1$, $Z_1(G)=Z(G)$, and $Z_{i+1}(G)$ by $Z_{i+1}(G)/Z_i(G)=Z(G/Z_i(G))$. The chain $Z_0(G)\leq Z_1(G)\leq Z_2(G)\leq\cdots$ is called the upper central series of $G$. A group $G$ is called nilpotent if $Z_c(G)=G$ for some $c\in\mathbb Z$.