Topology of subgroup lattices of symmetric and alternating groups

John Shareshian

doi:10.1016/S0097-3165(03)00138-9

Topology of subgroup lattices of symmetric and alternating groups

John Shareshian

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Abstract

We determine the homotopy type of the order complex of the subgroup lattice of the symmetric group S_n when n is a prime or a power of two. (The prime case has been treated previously in unpublished work of G. Ivanyos.) We do the same for alternating groups of prime degree. In addition, we show that, for any n > 1, the homology of the order complex of the subgroup lattice of S_n has rank at least n!/2 in dimension n - 3.

Original language	English
Pages (from-to)	137-155
Number of pages	19
Journal	Journal of Combinatorial Theory. Series A
Volume	104
Issue number	1
DOIs	https://doi.org/10.1016/S0097-3165(03)00138-9
State	Published - Oct 2003

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title = "Topology of subgroup lattices of symmetric and alternating groups",

abstract = "We determine the homotopy type of the order complex of the subgroup lattice of the symmetric group Sn when n is a prime or a power of two. (The prime case has been treated previously in unpublished work of G. Ivanyos.) We do the same for alternating groups of prime degree. In addition, we show that, for any n > 1, the homology of the order complex of the subgroup lattice of Sn has rank at least n!/2 in dimension n - 3.",

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N2 - We determine the homotopy type of the order complex of the subgroup lattice of the symmetric group Sn when n is a prime or a power of two. (The prime case has been treated previously in unpublished work of G. Ivanyos.) We do the same for alternating groups of prime degree. In addition, we show that, for any n > 1, the homology of the order complex of the subgroup lattice of Sn has rank at least n!/2 in dimension n - 3.

AB - We determine the homotopy type of the order complex of the subgroup lattice of the symmetric group Sn when n is a prime or a power of two. (The prime case has been treated previously in unpublished work of G. Ivanyos.) We do the same for alternating groups of prime degree. In addition, we show that, for any n > 1, the homology of the order complex of the subgroup lattice of Sn has rank at least n!/2 in dimension n - 3.

UR - https://www.scopus.com/pages/publications/0344152928

U2 - 10.1016/S0097-3165(03)00138-9

DO - 10.1016/S0097-3165(03)00138-9

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AN - SCOPUS:0344152928

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VL - 104

SP - 137

EP - 155

JO - Journal of Combinatorial Theory. Series A

JF - Journal of Combinatorial Theory. Series A

IS - 1

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Topology of subgroup lattices of symmetric and alternating groups

Abstract

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