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Topology of order complexes of intervals in subgroup lattices

✍ Scribed by John Shareshian

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
183 KB
Volume
268
Category
Article
ISSN
0021-8693

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✦ Synopsis

We conjecture that the order complex of an open interval in the subgroup lattice of a finite group has the homotopy type of a wedge of spheres and prove that if (H, G) is a minimal counterexample to this conjecture then either G is almost simple or G = H N, where N is the unique minimal normal subgroup of G, N is non-Abelian and H ∩ N = 1.

πŸ“œ SIMILAR VOLUMES

On Representing Finite Lattices as Inter
On Representing Finite Lattices as Intervals in Subgroup Lattices of Finite Groups
✍ Robert Baddeley; Andrea Lucchini πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 832 KB

Let M M be the lattice of length 2 with n G 1 atoms. It is an open problem to n Ε½ decide whether or not every such lattice or indeed whether or not every finite . lattice can be represented as an interval in the subgroup lattice of some finite group. We complete the work of the second author, Lucchi

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