Acyclic 2-dimensional complexes and Quillen's conjecture
Piterman, Kevin Iván (Universidad de Buenos Aires. Departamento de Matemática)
Sadofschi Costa, Iván (Universidad de Buenos Aires. Instituto de Matematica Luis Santaló)
Viruel Arbáizar, Antonio (Universidad de Málaga. Departamento de Álgebra, Geometría y Topología)

Date:	2021
Abstract:	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 seminal work of Aschbacher-Smith.
Grants:	Ministerio de Economía y Competitividad MTM2016-78647-P
Note:	This work was partially done at the University of Málaga, during a research stay of the first two authors, supported by project MTM2016-78647-P. The first author was supported by a CONICET doctoral fellowship and grants CONICET PIP 112201701 00357CO and UBACyT 20020160100081BA. The second author was supported by a CONICET postdoctoral fellowship and grants ANPCyT PICT-2017-2806, CONICET PIP 11220170100357CO, and UBACyT 20020160100081BA. The third author was partially supported by Ministerio de Economía y Competitividad (Spain), grant MTM2016-78647-P (AEI/FEDER, UE, support included).
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	Quillen's conjecture ; Poset ; P-subgroups
Published in:	Publicacions matemàtiques, Vol. 65 Núm. 1 (2021) , p. 129-140 (Articles) , ISSN 2014-4350

Adreça alternativa: https://raco.cat/index.php/PublicacionsMatematiques/article/view/383687
DOI: 10.5565/PUBLMAT6512104

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