Quillen's conjecture and unitary groups
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866911556785143808 |
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| author | Ramos, Antonio Díaz |
| author_facet | Ramos, Antonio Díaz |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_15613 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Quillen's conjecture and unitary groups Ramos, Antonio Díaz Algebraic Topology Group Theory 55U10, 05E45, 20J99 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. |
| title | Quillen's conjecture and unitary groups |
| topic | Algebraic Topology Group Theory 55U10, 05E45, 20J99 |
| url | https://arxiv.org/abs/2303.15613 |