Shelling the coset poset. (Q880012)
From MaRDI portal
scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Shelling the coset poset. |
scientific article |
Statements
Shelling the coset poset. (English)
0 references
10 May 2007
0 references
The main goal of this paper is to study some remarkable properties of the coset lattice of a finite group. It is proved that this lattice has shellable order complex if and only if the group is complemented. Moreover, this lattice possesses a Cohen-Macaulay order complex under the same conditions. Some interesting examples and open problems (further research directions) are also presented in the end of the paper.
0 references
lexicographic shellings
0 references
coset posets
0 references
coset lattices
0 references
subgroup lattices
0 references
complemented groups
0 references
finite groups
0 references
order complexes
0 references
