Shelling the Coset Poset

Abstract

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.

14 pages, 3 figures; Improved exposition of Lemma 4.1, other minor fixes. Submitted to Journal of Combinatorial Theory, Series A

References in corpus (2)

• Lectures on 0/1-polytopes
• Connectivity of the coset poset and the subgroup poset of a group

Cited by in corpus (3)

• Order complexes of coset posets of finite groups are not contractible
• Cubical convex ear decompositions
• On Boolean intervals of finite groups