Acyclic 2-dimensional complexes and Quillen’s conjecture

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Kevin Ivan Piterman
Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matem´atica
Iv´an Sadofschi Costa
CONICET-Universidad de Buenos Aires. Instituto de Investigaciones Matem´aticas Luis A. Santal´o (IMAS)
Antonio Viruel Arbáizar
Universidad de Málaga. Departamento de Algebra, Geometría y Topología
https://orcid.org/0000-0002-1605-5845

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.

Paraules clau
Quillen’s conjecture, poset, p-subgroups

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Com citar
Piterman, Kevin Ivan et al. «Acyclic 2-dimensional complexes and Quillen’s conjecture». Publicacions Matemàtiques, 2021, vol.VOL 65, núm. 1, p. 129–140, http://raco.cat/index.php/PublicacionsMatematiques/article/view/383687.
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