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


Author: John Shareshian
Journal: Trans. Amer. Math. Soc. 353 (2001), 2689-2703
MSC (1991): Primary 06A11; Secondary 20E15
DOI: https://doi.org/10.1090/S0002-9947-01-02730-1
Published electronically: March 12, 2001
MathSciNet review: 1828468
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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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Additional Information

John Shareshian
Affiliation: California Institute of Technology, Pasadena, California 91125
Address at time of publication: Department of Mathematics, University of Miami, Coral Gables, Florida 33124
Email: shareshi@math.miami.edu

DOI: https://doi.org/10.1090/S0002-9947-01-02730-1
Received by editor(s): February 18, 1999
Received by editor(s) in revised form: May 1, 1999
Published electronically: March 12, 2001
Article copyright: © Copyright 2001 American Mathematical Society

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