The poset of conjugacy classes of subgroups in a finite solvable group

DOI10.1016/0021-8693(92)90243-FzbMath0827.20028OpenAlexW2077833277MaRDI QIDQ1188132

Volkmar Welker

Publication date: 13 August 1992

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-8693(92)90243-f

zbMATH Keywords

finite solvable groupshomotopy typeconjugacy classes of subgroupsQuillen complexMöbius numberprefrattini groups

Mathematics Subject Classification ID

Finite solvable groups, theory of formations, Schunck classes, Fitting classes, (pi)-length, ranks (20D10) Arithmetic and combinatorial problems involving abstract finite groups (20D60) Special subgroups (Frattini, Fitting, etc.) (20D25) Series and lattices of subgroups (20D30) Combinatorics of partially ordered sets (06A07)

Related Items

Equivariant homotopy of posets and some applications to subgroup lattices ⋮ Combinatorial properties of intervals in finite solvable groups ⋮ The combinatorics and the homology of the poset of subgroups of \(p\)-power index

Cites Work

• Unnamed Item
• Die Eulersche Funktion endlicher auflösbarer Gruppen
• 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.
• Homotopy properties of the poset of nontrivial p-subgroups of a group
• Die Praefrattinigruppe im Intervall eines Untergruppenverbandes. (The prefrattini group in the interval of a subgroup lattice)
• A homotopy complementation formula for partially ordered sets
• [https://portal.mardi4nfdi.de/wiki/Publication:5731810 On the foundations of combinatorial theory I. Theory of M�bius Functions]
• On the Möbius function of a finite group