Journal of Group Theory | 2021
A geometric approach to Quillen’s conjecture
Abstract
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.\u2009D. Smith, On Quillen’s conjecture for the 𝑝-groups complex, Ann. of Math. (2)137 (1993), 3, 473–529], our techniques are simpler.