derived series

《Abstract Algebra》 · 第 194 页 · Section 6.1「$p$-groups, Nilpotent Groups, and Solvable Groups」，Definition

For any group $G$ define the following sequence of subgroups inductively: $G^{(0)}=G$, $G^{(1)}=[G,G]$ and $G^{(i+1)}=[G^{(i)},G^{(i)}]$ for all $i\geq 1$. This series of subgroups is called the derived or commutator series of $G$.