The combinatorics and the homology of the poset of subgroups of \(p\)-power index

DOI10.1016/0022-4049(93)90044-TzbMath0812.20006MaRDI QIDQ1313798

Volkmar Welker, Michael Weidner

Publication date: 9 May 1995

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

zbMATH Keywords

finite groupshomotopy typehomologyorder complexgeometric realizationhomotopy equivalentMöbius numberCL-shellablehomotopy wedge of spheresprime power indexshellability theory of posetssubgroup posets

Mathematics Subject Classification ID

Related Items (2)

Combinatorial properties of intervals in finite solvable groups ⋮ On the poset of conjugacy classes of subgroups of π-power index

Cites Work

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• Praefrattinigruppen und Matroide. (Prefrattinigroups and matroids)
• Subgroups of prime power index in a simple group
• Type d'homotopie des treillis et treillis des sous-groupes d'un groupe fini. (Homotopy type of lattices and lattices of subgroups of a finite groups)
• Pre-Frattini groups.
• Some aspects of groups acting on finite posets
• Homotopy equivalence of posets with a group action
• The poset of conjugacy classes of subgroups in a finite solvable group
• Galois connections between subgroup lattices and module lattices
• Homotopy properties of the poset of nontrivial p-subgroups of a group
• Equivariant homotopy of posets and some applications to subgroup lattices
• On Quillen's conjecture for the \(p\)-groups complex
• Die Praefrattinigruppe im Intervall eines Untergruppenverbandes. (The prefrattini group in the interval of a subgroup lattice)
• A homotopy complementation formula for partially ordered sets
• On Lexicographically Shellable Posets
• [https://portal.mardi4nfdi.de/wiki/Publication:5731810 On the foundations of combinatorial theory I. Theory of M�bius Functions]

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