Galois group
The Galois group of a field extension is the group of all field automorphisms of which fix (i.e., for all ). The group operation is given by composition: for two automorphisms , given by and , the product is the composite of the two maps .
The Galois group of a polynomial is defined to be the Galois group of the splitting field of over .
Title | Galois group |
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Canonical name | GaloisGroup |
Date of creation | 2013-03-22 12:08:19 |
Last modified on | 2013-03-22 12:08:19 |
Owner | djao (24) |
Last modified by | djao (24) |
Numerical id | 8 |
Author | djao (24) |
Entry type | Definition |
Classification | msc 12F10 |
Related topic | FundamentalTheoremOfGaloisTheory |
Related topic | InfiniteGaloisTheory |