Quillen's conjecture on the poset of elementary abelian p-subgroups

Let $G$ be a finite group and let $p$ be a prime dividing $|G|$. Let ${\mathcal{A}}_p(G)$ be the poset of non-trivial elementary abelian $p$-subgroups of $G$, ordered by inclusion, and let $|{\mathcal{A}}_p(G)|$ denote its geometric realization. Let $O_p(G)$ be the largest normal $p$-subgroup of $G$. Quillen's conjecture. If $|{\mathcal{A}}_p(G)|$ is contractible, then $O_p(G)\neq 1$. This is Quillen's conjecture relating the topology of the poset of elementary abelian $p$-subgroups to the existence of a nontrivial normal $p$-subgroup. The paper proves a strong version of the conjecture for most finite classical groups in non-defining characteristic, but the stated implication is not resolved in full generality here.