On a conjecture of Quillen and a lemma of Robinson

DOI10.1007/BF01191159zbMath0723.20012OpenAlexW2031506227WikidataQ122899714 ScholiaQ122899714MaRDI QIDQ757589

Michael Aschbacher, Peter B. Kleidman

Publication date: 1990

Published in: Archiv der Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01191159

zbMATH Keywords

finite groupssimplicial complexes\(p\)-subgroupscomponentsalmost simple finite groupsnilpotent \(p'\)-subgroupsRobinson property

Mathematics Subject Classification ID

Arithmetic and combinatorial problems involving abstract finite groups (20D60) Series and lattices of subgroups (20D30) Finite simple groups and their classification (20D05) Finite nilpotent groups, (p)-groups (20D15)

Related Items (12)

Eliminating components in Quillen's conjecture ⋮ Unnamed Item ⋮ A generalisation of a theorem of Wielandt ⋮ 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 ⋮ Simple connectivity of \(p\)-group complexes ⋮ Group actions on finite acyclic simplicial complexes ⋮ Equivariant \(K\)-theory and Alperin's conjecture ⋮ An approach to Quillen’s conjecture via centralisers of simple groups

Cites Work

• Unnamed Item
• The root subgroups for maximal tori in finite groups of Lie type
• Some remarks on permutation modules
• Homotopy properties of the poset of nontrivial p-subgroups of a group
• Éléments unipotents et sous-groupes paraboliques de groupes réductifs. I
• The local structure of finite groups of characteristic 2 type
• Overgroups of Sylow subgroups in sporadic groups
• Involutions in Chevalley groups over fields of even order

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