On the shellability of the order complex of the subgroup lattice of a finite group

Shareshian, John

doi:10.1090/S0002-9947-01-02730-1

On the shellability of the order complex of the subgroup lattice of a finite group
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Trans. Amer. Math. Soc. 353 (2001), 2689-2703 Request permission

Abstract:

We show that the order complex of the subgroup lattice of a finite group $G$ is nonpure shellable if and only if $G$ is solvable. A by-product of the proof that nonsolvable groups do not have shellable subgroup lattices is the determination of the homotopy types of the order complexes of the subgroup lattices of many minimal simple groups.

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