See Galois group on Wiktionary
{
"etymology_text": "Named after Évariste Galois, who first discovered them.",
"forms": [
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"form": "Galois groups",
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"name": "Algebra",
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"examples": [
{
"ref": "1996, Patrick Morandi, Field and Galois Theory, Springer, page 123:",
"text": "In this section, we show how to determine the Galois group and the roots of an irreducible polynomial of degree 2, 3, or 4.",
"type": "quote"
},
{
"ref": "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:",
"text": "Let B be a Galois algebra over R with Galois group G, C the center of B, and K#x3D;#x5C;#x7B;g#x5C;inG#x5C;vertg(c)#x3D;c#x5C;#x5C;mathsf#x7B;for#x5C;each#x7D;#x5C;c#x5C;inC#x5C;#x7D;. A natural question is whether B is a central Galois algebra with Galois group K.",
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{
"ref": "2009, Steven H. Weintraub, Galois Theory, 2nd edition, Springer, page 128:",
"text": "Our work actually gives an algorithm for computing Galois groups of polynomials f(X)#x5C;in#x5C;Q#x5B;X#x5D;:",
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}
],
"glosses": [
"The automorphism group of a Galois extension."
],
"id": "en-Galois_group-en-noun-WBEU9lYb",
"links": [
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"algebra",
"algebra"
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"automorphism group",
"automorphism group"
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"Galois extension",
"Galois extension"
]
],
"qualifier": "Galois theory",
"raw_glosses": [
"(algebra, Galois theory) The automorphism group of a Galois extension."
],
"related": [
{
"word": "Galois algebra"
},
{
"word": "Galois closure"
},
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"word": "Galois extension"
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{
"word": "Galois theory"
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"translations": [
{
"code": "ar",
"lang": "Arabic",
"sense": "specific group associated with a field extension",
"word": "زمرة غالوا"
},
{
"code": "cmn",
"lang": "Chinese Mandarin",
"sense": "specific group associated with a field extension",
"word": "伽罗瓦群"
},
{
"code": "fr",
"lang": "French",
"sense": "specific group associated with a field extension",
"word": "groupe de Galois"
},
{
"code": "hu",
"lang": "Hungarian",
"sense": "specific group associated with a field extension",
"word": "Galois-csoport"
},
{
"code": "it",
"lang": "Italian",
"sense": "specific group associated with a field extension",
"tags": [
"masculine"
],
"word": "gruppo di Galois"
},
{
"code": "ja",
"lang": "Japanese",
"sense": "specific group associated with a field extension",
"word": "ガロア群"
},
{
"code": "ko",
"lang": "Korean",
"roman": "gallua gun",
"sense": "specific group associated with a field extension",
"word": "갈루아 군"
},
{
"code": "ru",
"lang": "Russian",
"roman": "gruppa Galua",
"sense": "specific group associated with a field extension",
"word": "группа Галуа"
},
{
"code": "es",
"lang": "Spanish",
"sense": "specific group associated with a field extension",
"word": "grupo de Galois"
}
],
"wikipedia": [
"Galois group",
"Évariste Galois"
]
}
],
"word": "Galois group"
}
{
"etymology_text": "Named after Évariste Galois, who first discovered them.",
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"ref": "1996, Patrick Morandi, Field and Galois Theory, Springer, page 123:",
"text": "In this section, we show how to determine the Galois group and the roots of an irreducible polynomial of degree 2, 3, or 4.",
"type": "quote"
},
{
"ref": "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:",
"text": "Let B be a Galois algebra over R with Galois group G, C the center of B, and K#x3D;#x5C;#x7B;g#x5C;inG#x5C;vertg(c)#x3D;c#x5C;#x5C;mathsf#x7B;for#x5C;each#x7D;#x5C;c#x5C;inC#x5C;#x7D;. A natural question is whether B is a central Galois algebra with Galois group K.",
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"ref": "2009, Steven H. Weintraub, Galois Theory, 2nd edition, Springer, page 128:",
"text": "Our work actually gives an algorithm for computing Galois groups of polynomials f(X)#x5C;in#x5C;Q#x5B;X#x5D;:",
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],
"glosses": [
"The automorphism group of a Galois extension."
],
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"qualifier": "Galois theory",
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"(algebra, Galois theory) The automorphism group of a Galois extension."
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"translations": [
{
"code": "ar",
"lang": "Arabic",
"sense": "specific group associated with a field extension",
"word": "زمرة غالوا"
},
{
"code": "cmn",
"lang": "Chinese Mandarin",
"sense": "specific group associated with a field extension",
"word": "伽罗瓦群"
},
{
"code": "fr",
"lang": "French",
"sense": "specific group associated with a field extension",
"word": "groupe de Galois"
},
{
"code": "hu",
"lang": "Hungarian",
"sense": "specific group associated with a field extension",
"word": "Galois-csoport"
},
{
"code": "it",
"lang": "Italian",
"sense": "specific group associated with a field extension",
"tags": [
"masculine"
],
"word": "gruppo di Galois"
},
{
"code": "ja",
"lang": "Japanese",
"sense": "specific group associated with a field extension",
"word": "ガロア群"
},
{
"code": "ko",
"lang": "Korean",
"roman": "gallua gun",
"sense": "specific group associated with a field extension",
"word": "갈루아 군"
},
{
"code": "ru",
"lang": "Russian",
"roman": "gruppa Galua",
"sense": "specific group associated with a field extension",
"word": "группа Галуа"
},
{
"code": "es",
"lang": "Spanish",
"sense": "specific group associated with a field extension",
"word": "grupo de Galois"
}
],
"word": "Galois group"
}
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