Shelling The Coset Poset
Woodroofe, Russell S
It is shown that the coset lattice of a finite group has shellable order complex if and only if the group is complemented. It is also shown that the order complex is Cohen-Macaulay under the same circumstances. The group theoretical tools used are relatively elementary, and avoid the classification of finite simple groups and of minimal finite simple groups.
group theory; combinatorics; poset; complemented group; coset
Previously Published As
Russ Woodroofe, Shelling the coset poset, 2003, arXiv:math.NT/9810036
dissertation or thesis