Galois group

From Wiktionary, the free dictionary
Jump to navigation Jump to search

English

[edit]
English Wikipedia has an article on:
Wikipedia

Etymology

[edit]

Named after Évariste Galois, who first discovered them.

Noun

[edit]

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

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

Translations

[edit]

See also

[edit]

Further reading

[edit]