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Galois group of the compositum of two Galois extensions
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(Theorem)
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Corollary 1 Let $E$ and $F$ be Galois extensions of a field $K$ such that $E\cap F=K$ . Then $EF$ is Galois over $K$ and the Galois group is isomorphic to the direct product: $$\Gal(EF/K)\cong \Gal(E/K) \times \Gal(F/K).$$
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"Galois group of the compositum of two Galois extensions" is owned by alozano.
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Cross-references: restrictions, direct product, subgroup, isomorphic, Galois group, compositum, intersection, field, Galois extensions
There are 2 references to this entry.
This is version 2 of Galois group of the compositum of two Galois extensions, born on 2005-02-22, modified 2005-03-10.
Object id is 6794, canonical name is GaloisGroupOfTheCompositumOfTwoGaloisExtensions.
Accessed 2110 times total.
Classification:
| AMS MSC: | 12F99 (Field theory and polynomials :: Field extensions :: Miscellaneous) | | | 11R32 (Number theory :: Algebraic number theory: global fields :: Galois theory) |
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Pending Errata and Addenda
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