# Cyclic extension

## Homework Statement

Let K be a field, and let K' be an algebraic closure of K. Let sigma be
an automorphism of K' over K, and let F be the fix field of sigma. Let L/F
be any finite extension of F.

## Homework Equations

Show that L/F is a finite Galois extension whose
Galois group Gal(L/F) is cyclic.