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On the shellability of the order complex of the subgroup lattice of a finite group |
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| Authors: | John Shareshian |
| Affiliation: | California Institute of Technology, Pasadena, California 91125 |
| Abstract: | We show that the order complex of the subgroup lattice of a finite group |
| Keywords: | |
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is nonpure shellable if and only if 
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.