Simple connectivity of \(p\)-group complexes

DOI10.1007/BF02808107zbMath0829.20031MaRDI QIDQ689843

Michael Aschbacher

Publication date: 15 January 1996

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

sporadic groupsfinite groupshomotopy typealternating groupsrankstrongly \(p\)-embedded subgroupsgroups of Lie typecommuting graphMathieu groupssimple componentsQuillen complexcommuting subgroupsBrown complexcommuting complexconnected commuting complexelementary Abelian \(p\)- subgroupssimple connectivity of simplicial complexessubgroups of order \(p\)

Mathematics Subject Classification ID

Simple groups: sporadic groups (20D08) Sylow subgroups, Sylow properties, (pi)-groups, (pi)-structure (20D20) Series and lattices of subgroups (20D30) Homotopy equivalences in algebraic topology (55P10) Homological methods in group theory (20J05) Simple groups: alternating groups and groups of Lie type (20D06) Simplicial sets and complexes in algebraic topology (55U10)

Related Items

Endotrivial modules for finite groups via homotopy theory ⋮ Simply connected coset complexes for rank 1 groups of Lie type ⋮ The fundamental group of the Quillen complex of the symmetric group ⋮ Finite groups and subgroup-permutability ⋮ Radical 3-subgroups of \(F_4(q)\) with \(q\) even. ⋮ Simple connectivity of the Quillen complex of the symmetric group. ⋮ The homotopy types of the posets of \(p\)-subgroups of a finite group ⋮ The essential rank of classical groups. ⋮ The coset poset and probabilistic zeta function of a finite group ⋮ A stronger reformulation of Webb's conjecture in terms of finite topological spaces ⋮ Group actions on finite acyclic simplicial complexes ⋮ On the homotopy type of the Quillen complex of finite soluble groups ⋮ The AWC-goodness and essential rank of sporadic simple groups. ⋮ Locally connected simplicial maps ⋮ Classification of Finite Groups with Toroidal or Projective-Planar Permutability Graphs ⋮ Some results about Quillen complex of \(\text{Sp}_{2n}(q)\) ⋮ Hypergraph matching complexes and Quillen complexes of symmetric groups. ⋮ An approach to Quillen’s conjecture via centralisers of simple groups ⋮ The fundamental group of the p‐subgroup complex

Cites Work

• On a conjecture of Quillen and a lemma of Robinson
• Flag structures on Tits geometries
• Extending morphisms of groups and graphs
• Homotopy properties of the poset of nontrivial p-subgroups of a group
• Some remarks on finite 1-acyclic and collapsible complexes
• Locally connected simplicial maps
• The local structure of finite groups of characteristic 2 type
• Overgroups of Sylow subgroups in sporadic groups
• The Uniqueness of Groups of Lyons Type
• Finite Groups With a Proper 2-Generated Core
• Finite groups whose 2-subgroups are generated by at most 4 elements
• Involutions in Chevalley groups over fields of even order
• Bender Groups as Standard Subgroups
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item