Shelling the Coset Poset
Group Theory
2011-01-27 v4 Combinatorics
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.
Cite
@article{arxiv.math/0306346,
title = {Shelling the Coset Poset},
author = {Russ Woodroofe},
journal= {arXiv preprint arXiv:math/0306346},
year = {2011}
}
Comments
14 pages, 3 figures; Improved exposition of Lemma 4.1, other minor fixes. Submitted to Journal of Combinatorial Theory, Series A