Galois group en · NOUN
Etymology
Named after Évariste Galois, who first discovered them.
Meanings
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(qualifier:Galois theory) The 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: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: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:
Forms
| Spelling | Features | Labels | Source |
|---|---|---|---|
| Galois groups | Number=Plur | lexicographic |
Relateds
Galois closure · Galois theory · Galois extension · Galois algebra
Translations (11)
ar زمرة غالوا (specific group associated with a field extension) · es grupo de Galois (specific group associated with a field extension) · cmn 伽罗瓦群 (specific group associated with a field extension) · ko 갈루아 군 (specific group associated with a field extension) · hu Galois-csoport (specific group associated with a field extension) · ja ガロア群 (specific group associated with a field extension) · fr groupe de Galois (specific group associated with a field extension) · it gruppo di Galois (specific group associated with a field extension) · pl grupa Galois (specific group associated with a field extension) · ru группа Галуа (specific group associated with a field extension) · fi Galois’n ryhmä (specific group associated with a field extension)