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

John Shareshian

doi:10.1090/s0002-9947-01-02730-1

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

John Shareshian

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24 Scopus citations

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.

Original language	English
Pages (from-to)	2689-2703
Number of pages	15
Journal	Transactions of the American Mathematical Society
Volume	353
Issue number	7
DOIs	https://doi.org/10.1090/s0002-9947-01-02730-1
State	Published - 2001

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10.1090/s0002-9947-01-02730-1

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

Abstract

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