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Shelling the Coset Poset

Russ Woodroofe
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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.

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Russ Woodroofe. 2003-06-24. Shelling the Coset Poset. https://doi.org/10.1016/j.jcta.2006.08.010

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