Definition 8

A group G is called solvable if there exists an integer n such that $D^n(G) = \{e\}$. If G is a solvable group, the least integer n such that $D^n(G) = \{e\}$ is called the solvability class of G.

A solvable group of solvability class $n$ is called a solvable group of class $n$. A group is sometimes said to be of finite solvability class if it is solvable.