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Realizability and automatic realizability of Galois groups of order 32

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Central European Journal of Mathematics

Abstract

This article provides necessary and sufficient conditions for each group of order 32 to be realizable as a Galois group over an arbitrary field. These conditions, given in terms of the number of square classes of the field and the triviality of specific elements in related Brauer groups, are used to derive a variety of automatic realizability results.

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Authors and Affiliations

  1. Bryn Mawr College, Bryn Mawr, PA, 19010, USA

    Helen G. Grundman

  2. University of Cincinnati, Cincinnati, OH, 45221, USA

    Tara L. Smith

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  1. Helen G. Grundman
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  2. Tara L. Smith
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Correspondence to Helen G. Grundman.

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Grundman, H.G., Smith, T.L. Realizability and automatic realizability of Galois groups of order 32. centr.eur.j.math. 8, 244–260 (2010). https://doi.org/10.2478/s11533-009-0072-x

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  • DOI: https://doi.org/10.2478/s11533-009-0072-x

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