N-solvable group

Definition
Suppose $$G$$ is a group and $$n$$ is an integer. We say that $$G$$ is $$n$$-solvable if the n-derived series of $$G$$ reaches the trivial subgroup in finitely many steps. The number of steps it takes to do so is termed the n-derived length of $$G$$.

Terminology caution
Note that the notion of n-solvable group is distinct from the notion of p-solvable group. In particular, when somebody talks of $$n$$-solvability for a prime number $$n$$, it is more likely that they are referring to it in the sense of p-solvability rather than n-solvability as defined here.