On the shellability of the order complex of the subgroup lattice of a finite group

DOI10.1090/S0002-9947-01-02730-1zbMath0982.06004MaRDI QIDQ2719043

John Shareshian

Publication date: 14 May 2001

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

finite groupssolvabilitysimplicial complexorder complexsolvable groupsshellabilitysubgroup lattice

Mathematics Subject Classification ID

Solvable groups, supersolvable groups (20F16) Chains and lattices of subgroups, subnormal subgroups (20E15) Algebraic aspects of posets (06A11) Shellability for polytopes and polyhedra (52B22) Lattices (06B99)

Related Items

Discrete Morse functions from lexicographic orders ⋮ From the weak Bruhat order to crystal posets ⋮ Shelling the coset poset. ⋮ Chains of modular elements and shellability ⋮ A new subgroup lattice characterization of finite solvable groups. ⋮ A lexicographic shellability characterization of geometric lattices ⋮ Topology of order complexes of intervals in subgroup lattices. ⋮ Topology of subgroup lattices of symmetric and alternating groups. ⋮ An 𝐸𝐿-labeling of the subgroup lattice ⋮ TANGLE SUM AND CONSTRUCTIBLE SPHERES ⋮ Homotopy types of group lattices ⋮ The coset poset and probabilistic zeta function of a finite group ⋮ Linear inequalities for enumerating chains in partially ordered sets ⋮ A broad class of shellable lattices ⋮ On commuting and noncommuting complexes ⋮ EL-shelling on comodernistic lattices ⋮ Homotopy classification of actions of finite groups on aspherical spaces. ⋮ Koszul incidence algebras, affine semigroups, and Stanley-Reisner ideals. ⋮ A characterization of solvability for finite groups in terms of their frame. ⋮ Shellings from relative shellings, with an application to NP-completeness ⋮ Unnamed Item ⋮ Simplicial shellable spheres via combinatorial blowups

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The top homology of the lattice of subgroups of a soluble 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)
• Finite soluble groups
• Homotopy properties of the poset of nontrivial p-subgroups of a group
• Supersolvable lattices
• Shellable and Cohen-Macaulay Partially Ordered Sets
• The MÖBius Function of Psl₂ (q ), with Application to the Maximal Normal Subgroups of the Modular Group
• Shellable Nonpure Complexes and Posets. I
• Nonsolvable finite groups all of whose local subgroups are solvable
• THE EULERIAN FUNCTIONS OF A GROUP
• On a class of doubly transitive groups