fixed field
FixedField
2002-01-05 02:30:40
2002-08-22 07:57:05
Definition
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Let $K/F$ be a field extension with Galois group $G = \operatorname{Gal}(K/F)$, and let $H$ be a subgroup of $G$. The {\em fixed field} of $H$ in $K$ is the set
$$
K^H := \{ x \in K \mid \sigma(x) = x\text{ for all }\sigma \in H \}.
$$
The set $K^H$ is always a field, and $F \subset K^H \subset K$.