Let $\pi$ be a set of prime numbers. A finite group $G$ is called $\pi$ separable if there exists a composition series $$ \{1\}=G_0\lhd\cdots\lhd G_n=G $$ such that each $G_{i+1}/G_i$ is either a $\pi$ group or a $\pi'$ group.

A $\{p\}$ separable group, where $p$ is a prime number, is usually called a $p$ separable group.

$\pi$ separability can be thought of as a generalization of solvability for finite groups; a finite group is $\pi$ separable for all sets of primes if and only it is solvable.