Galois group
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English
[edit]Etymology
[edit]Named after Évariste Galois, who first discovered them.
Noun
[edit]Galois group (plural Galois groups)
- (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
[edit]- The automorphism group of a Galois extension may be denoted .
- is the trivial group whose single element is the identity automorphism.
Translations
[edit]specific group associated with a field extension
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See also
[edit]Further reading
[edit]- Galois theory on Wikipedia.Wikipedia
- Galois closure on Wikipedia.Wikipedia
- Galois extension on Wikipedia.Wikipedia