  We introduce {\em admissible collections} for a finite group $G$ and use them
to prove that most of the finite classical groups in non-defining
characteristic satisfy the {\em Quillen dimension at $p$ property}, a strong
version of Quillen's conjecture, at a given odd prime divisor $p$ of $|G|$.
Compared to the methods in \cite{AS1993}, our techniques are simpler.
