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arXiv · 2303.15613

Quillen's conjecture and unitary groups

Antonio Díaz Ramos
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Abstract

We prove that the Quillen posets $\mathcal{A}_p(H)$ of $p$-extensions $H$ of simple unitary groups have non-zero homology in the largest possible dimension, with just a few exceptions. This establishes a conjecture raised by Aschbacher-Smith in 1992. In particular, by their work and a more recent article by Piterman-Smith, Quillen's conjecture on the $p$-subgroup posets holds for odd primes.

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Antonio Díaz Ramos. 2023-03-27. Quillen's conjecture and unitary groups. https://arxiv.org/abs/2303.15613

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