Abstract
We introduce 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
Quillen dimension at 𝑝 property, a strong version of Quillen’s conjecture, at a given odd prime divisor 𝑝 of
|
G
|
\lvert G\rvert
.
Compared to the methods in [M. Aschbacher and S. D. Smith, On Quillen’s conjecture for the 𝑝-groups complex, Ann. of Math. (2)
137 (1993), 3, 473–529], our techniques are simpler.