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fixed field (Definition)

Let $ K/F$ be a field extension with Galois group $ G = \operatorname{Gal}(K/F)$, and let $ H$ be a subgroup of $ G$. The fixed field of $ H$ in $ K$ is the set

$\displaystyle K^H := \{ x \in K \mid \sigma(x) = x$ for all $\displaystyle \sigma \in H \}. $
The set $ K^H$ is always a field, and $ F \subset K^H \subset K$.



"fixed field" is owned by djao. [ full author list (2) ]
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Cross-references: field, subgroup, Galois group, field extension
There are 23 references to this entry.

This is version 2 of fixed field, born on 2002-01-05, modified 2002-08-22.
Object id is 1325, canonical name is FixedField.
Accessed 3167 times total.

Classification:
AMS MSC12F10 (Field theory and polynomials :: Field extensions :: Separable extensions, Galois theory)

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