Galois group

noun

The automorphism group of a Galois extension.

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Meanings

nounGalois group (plural Galois groups)

plural Galois groups

  1. Galois theoryalgebraThe automorphism group of a Galois extension.

    Our work actually gives an algorithm for computing Galois groups of polynomials f(X)#92;in#92;Q#91;X#93;:

    2009, Steven H. Weintraub, Galois Theory, 2nd edition, Springer, page 128
    2 more examples

    In this section, we show how to determine the Galois group and the roots of an irreducible polynomial of degree 2, 3, or 4.

    1996, Patrick Morandi, Field and Galois Theory, Springer, page 123

    Let B be a Galois algebra over R with Galois group G, C the center of B, and K#61;#92;#123;g#92;inG#92;vertg(c)#61;c#92;#92;mathsf#123;for#92;each#125;#92;c#92;inC#92;#125;. A natural question is whether B is a central Galois algebra with Galois group K.

    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

Origin

Named after Évariste Galois, who first discovered them.

Full word history & related roots →

Translations

Arabic زمرة غالوا
  • زمرة غالواspecific group associated with a field extension
Chinese Mandarin 伽罗瓦群
  • 伽罗瓦群specific group associated with a field extension
Finnish Galois’n ryhmä
  • Galois’n ryhmäspecific group associated with a field extension
French groupe de Galois
  • groupe de Galoisspecific group associated with a field extension
Hungarian Galois-csoport
  • Galois-csoportspecific group associated with a field extension
Italian gruppo di Galois
  • gruppo di Galoisspecific group associated with a field extension
Japanese ガロア群
  • ガロア群specific group associated with a field extension
Korean 갈루아 군
  • 갈루아 군 (gallua gun)specific group associated with a field extension
Polish grupa Galois
  • grupa Galoisspecific group associated with a field extension
Russian группа Галуа
  • группа Галуа (gruppa Galua)specific group associated with a field extension
Spanish grupo de Galois
  • grupo de Galoisspecific group associated with a field extension
Cite this entry
APA

Galois group. (n.d.). In WatkinsX Dictionary. Retrieved November 4, 2026, from https://dictionary.watkinsx.com/word/Galois%20group

MLA

“Galois group.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/Galois%20group. Accessed November 4, 2026.

Chicago

WatkinsX Dictionary, s.v. “Galois group,” accessed November 4, 2026, https://dictionary.watkinsx.com/word/Galois%20group.

Source: Galois group on Wiktionary, CC BY-SA 4.0.