Aschbacher's conjecture on simply connected p-subgroup complexes

Let $G$ be a finite group such that $G=AF^*(G)$, where $A$ is an elementary abelian $p$-subgroup of rank $r\geq 3$, and let $F^*(G)$ be the direct product of the $A$-conjugates of a simple component $L$ of $G$ whose order is prime to $p$. Aschbacher's conjecture. The complex ${\mathcal A}_p(G)$ is simply connected. This conjecture is used in the paper to reduce the study of freeness of the fundamental group of $p$-subgroup complexes to the almost simple case; the source treats it as an assumption in a main result.