Acyclic 2-dimensional complexes and Quillen’s conjecture
Acyclic 2-dimensional complexes and Quillen’s conjecture
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) = 1 for any group G admitting a G-invariant acyclic p-subgroup complex of dimension 2. In particular, it follows …