  Let $G$ be a finite group, $p$ a prime and $P$ a Sylow $p$-subgroup of $G$.
In this note we give a cohomological criterion for the $p$-solvability of $G$
depending on the cohomology in degree $1$ with coefficients in $\mathbb F_p$ of
both the normal subgroups of $G$ and $P$. As a byproduct we bound the minimal
number of quotients of order a power of $p$ appearing in any normal series of
$G$ by the number of generators of $P$.
