Derived length
= Derived length
{title2=$\min\{r:G^{(r)}=\{e\}\}$}
For a <solvable group>, its derived length is the least nonnegative <integer> $r$ at which the <derived series> reaches the trivial <group>, with $G^{(0)}=G$ and $G^{(r+1)}$ the <commutator subgroup> of $G^{(r)}$. A nontrivial <abelian group> has derived length one; a nonabelian <group> with nontrivial abelian <commutator subgroup> has derived length two.