Shelling the coset poset

It is shown that the coset lattice of a finite group has shellable order complex if and only if the group is complemented. Furthermore, the coset lattice is shown to have a Cohen–Macaulay order complex in exactly the same conditions. The group theoretical tools used are relatively elementary, and avoid the classification of finite simple groups and of minimal finite simple groups. © 2006 Elsevier Inc. All rights reserved.

• Type: Journal
• Year: 2007
• Where: JCT
• Authors: Russell Woodroofe
• Keywords: Coset Lattice, JCT 2007, Order Complex, finite Simple Groups