Quillen's conjecture and unitary groups

2023/03/27 by Antonio Díaz Ramos, Ramos, Antonio Díaz · 1 citation
Engineering · Mathematics · #Finite Group Theory Research #Rings, Modules, and Algebras #graph theory and CDMA systems #math.AT #math.GR

paper · pdf · doi:10.48550/arxiv.2303.15613

openalex publication_date 2023/03/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the Quillen posets 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.

Citations

• The local structure of finite groups of characteristic 2 type

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