On Quillen's conjecture for the \(p\)-groups complex

DOI10.2307/2946530zbMath0782.20039OpenAlexW2312969627WikidataQ123146185 ScholiaQ123146185MaRDI QIDQ1801592

Stephen D. Smith, Michael Aschbacher

Publication date: 10 March 1994

Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2946530

zbMATH Keywords

\(p\)-subgroupssimplicial complexfinite grouphomotopy equivalentcontractibleQuillen's conjecture

Mathematics Subject Classification ID

Series and lattices of subgroups (20D30) Homotopy equivalences in algebraic topology (55P10) Homological methods in group theory (20J05)

Related Items (18)

Endotrivial modules for finite groups via homotopy theory ⋮ Eliminating components in Quillen's conjecture ⋮ On the partially ordered set of nilpotent subgroups of a finite group ⋮ Euler characteristics and Möbius algebras of \(p\)-subgroup categories. ⋮ The homotopy types of the posets of \(p\)-subgroups of a finite group ⋮ Quillen's conjecture and the kernel on components ⋮ An algorithmic approach to fundamental groups and covers of combinatorial cell complexes ⋮ A stronger reformulation of Webb's conjecture in terms of finite topological spaces ⋮ Acyclic 2-dimensional complexes and Quillen's conjecture ⋮ On the homotopy type of the Quillen complex of finite soluble groups ⋮ On Quillen's conjecture for \(p\)-solvable groups ⋮ Finite solvable groups whose Quillen complex is Cohen-Macaulay. ⋮ A geometric approach to Quillen's conjecture ⋮ ON THE POSET OF NON-TRIVIAL PROPER SUBGROUPS OF A FINITE GROUP ⋮ An approach to Quillen’s conjecture via centralisers of simple groups ⋮ The fundamental group of the p‐subgroup complex ⋮ Top homology of hypergraph matching complexes, \(p\)-cycle complexes and Quillen complexes of symmetric groups. ⋮ The combinatorics and the homology of the poset of subgroups of \(p\)-power index

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