Shelling the Coset Poset

Details Shelling the Coset Poset Shelling the Coset Poset

2003-06-24

arxiv.org/abs/math/0306346v4

J. Comb. Theory Ser. A 114 (2007), no. 4, 733-746

Mathematics

Group Theory

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

Scientific paper

10.1016/j.jcta.2006.08.010

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.

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