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Sharply k-Transitive Permutation Groups Viewed as Galois Groups

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Abstract

The classification of finite sharply k-transitive groups was achieved by the efforts of Jordan (1873), Dickson (1905), and Zassenhaus (1936). Likewise for other families of finite groups, one expects that they are realizable as Galois groups over the field of rational numbers \({\mathbb{Q}}\). In this article, we study some properties of the polynomials \({f \in \mathbb{Q}[x]}\) such that the Galois group Gal(f) acts sharply k-transitively on its roots.

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Authors and Affiliations

  1. Departamento de Álgebra, Geometría y Topología, Universidad de Málaga, Málaga, Spain

    Mariángeles A. Gómez-Molleda

  2. Departament de Matemàtica Aplicada II, Universitat Politècnica de Catalunya, Barcelona, Spain

    Joan-C. Lario

Authors
  1. Mariángeles A. Gómez-Molleda
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  2. Joan-C. Lario
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Correspondence to Joan-C. Lario.

Additional information

Both authors partially supported by MICINN MTM2009-13060-C02-01.

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Gómez-Molleda, M.A., Lario, JC. Sharply k-Transitive Permutation Groups Viewed as Galois Groups. Mediterr. J. Math. 8, 617–632 (2011). https://doi.org/10.1007/s00009-010-0100-x

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  • DOI: https://doi.org/10.1007/s00009-010-0100-x

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