In terms of the Galois correspondence, a transitive group $G\leq S_n$ is the Galois group of an irreducible degree $n$ polynomial $f(x)\in K[x]$. Let $F=K(\alpha)$ where $\alpha$ is a root of $f(x)$. Then the **subfields** are intermediate fields for the extension $F/K$.

**Authors:**

**Knowl status:**

- Review status: reviewed
- Last edited by John Jones on 2018-07-09 22:54:29

**Referred to by:**

**History:**(expand/hide all)

- 2018-07-09 22:54:29 by John Jones (Reviewed)