Acyclic 2-dimensional complexes and Quillen’s conjecture

• Autores: Kevin Ivan Piterman, Iv´an Sadofschi Costa, Antonio Angel Viruel Arbaizar
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 65, Nº 1, 2021, págs. 129-140
• Idioma: inglés
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• Resumen

  • Let G be a finite group and Ap(G) be the poset of nontrivial elementary abelian p-subgroups of G. Quillen conjectured that Op(G) is nontrivial if Ap(G) is contractible. We prove that Op(G) 6= 1 for any group G admitting a G-invariant acyclic p subgroup complex of dimension 2. In particular, it follows that Quillen’s conjecture holds for groups of p-rank 3. We also apply this result to establish Quillen’s conjecture for some particular groups not considered in the seminalwork of Aschbacher–Smith.