Wythoff polytopes and low-dimensional homology of Mathieu groups

Mathieu Dutour Sikirić; Graham Ellis

doi:10.1016/j.jalgebra.2009.09.031

Wythoff polytopes and low-dimensional homology of Mathieu groups

Mathieu Dutour Sikirić
, Graham Ellis

Mathematics

Ruđer Bošković Institute

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

10 Citations (Scopus)

Abstract

We describe two methods for computing the low-dimensional integral homology of the Mathieu simple groups and use them to make computations such as H₅ (M₂₃, Z) = Z₇ and H₃ (M₂₄, Z) = Z₁₂. One method works via Sylow subgroups. The other method uses a Wythoff polytope and perturbation techniques to produce an explicit free Z M_n-resolution. Both methods apply in principle to arbitrary finite groups.

Original language	English
Pages (from-to)	4143-4150
Number of pages	8
Journal	Journal of Algebra
Volume	322
Issue number	11
DOIs	https://doi.org/10.1016/j.jalgebra.2009.09.031
Publication status	Published - 1 Dec 2009

Keywords

Group homology
Polytope
Resolution
Wythoff construction

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10.1016/j.jalgebra.2009.09.031

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abstract = "We describe two methods for computing the low-dimensional integral homology of the Mathieu simple groups and use them to make computations such as H5 (M23, Z) = Z7 and H3 (M24, Z) = Z12. One method works via Sylow subgroups. The other method uses a Wythoff polytope and perturbation techniques to produce an explicit free Z Mn-resolution. Both methods apply in principle to arbitrary finite groups.",

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N2 - We describe two methods for computing the low-dimensional integral homology of the Mathieu simple groups and use them to make computations such as H5 (M23, Z) = Z7 and H3 (M24, Z) = Z12. One method works via Sylow subgroups. The other method uses a Wythoff polytope and perturbation techniques to produce an explicit free Z Mn-resolution. Both methods apply in principle to arbitrary finite groups.

AB - We describe two methods for computing the low-dimensional integral homology of the Mathieu simple groups and use them to make computations such as H5 (M23, Z) = Z7 and H3 (M24, Z) = Z12. One method works via Sylow subgroups. The other method uses a Wythoff polytope and perturbation techniques to produce an explicit free Z Mn-resolution. Both methods apply in principle to arbitrary finite groups.

KW - Group homology

KW - Polytope

KW - Resolution

KW - Wythoff construction

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JO - Journal of Algebra

JF - Journal of Algebra

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Wythoff polytopes and low-dimensional homology of Mathieu groups

Abstract

Keywords

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