Definition A finite group $G$ is $\pi$-separable if has a series (supposed to be subnormal) where each factor is either a $\pi$-group of $\pi'$-group.
$\pi$ is a set of prime numbers and $\pi'$ is a set os prime numbers that are not in $\pi$.
This definitions comes from the Robinson's book "A Course in the Theory of Groups".
He says that a finite soluble group is $\pi$-separable for every $\pi$. How can I see it? Robinson says to refine the derived series inserting the $\pi$-component of each factor. Maybe this is a stupid question, but I cannot follow this explanation.