A geometric approach to Quillen's conjecture

Diaz Ramos, Antonio and Mazza, Nadia (2022) A geometric approach to Quillen's conjecture. Journal of Group Theory, 25 (1). pp. 91-112. ISSN 1433-5883

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Abstract

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.