English

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Etymology

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Named after Évariste Galois, who first discovered them.

Noun

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Galois group (plural Galois groups)

  1. (algebra, Galois theory) The automorphism group of a Galois extension.
    • 1996, Patrick Morandi, Field and Galois Theory, Springer, page 123:
      In this section, we show how to determine the Galois group and the roots of an irreducible polynomial of degree 2, 3, or 4.
    • 2004, George Szeto, Liangyong Xue, “On Central Galois Algebras of a Galois Algebra”, in Alberto Facchini, Evan Houston, Luigi Salce, editors, Rings, Modules, Algebras, and Abelian Groups, CRC Press, page 493:
      Let   be a Galois algebra over   with Galois group  ,   the center of  , and   A natural question is whether   is a central Galois algebra with Galois group  .
    • 2009, Steven H. Weintraub, Galois Theory, 2nd edition, Springer, page 128:
      Our work actually gives an algorithm for computing Galois groups of polynomials  :

Usage notes

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  • The automorphism group of a Galois extension   may be denoted  .
  •   is the trivial group whose single element is the identity automorphism.

Translations

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See also

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Further reading

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