Russ Woodroofe

Ph.D. (2005) Cornell University

First Position

Teaching Assistant, Weill Cornell Medical College at Qatar

Dissertation

Shelling the Coset Poset

Advisor:

Kenneth Brown

Research Area:

Group Theory and 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. 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.