Past exam of the mathematics course of the University of Cambridge / 2021 / ii / Paper 4 / 18I / a / Solution

An action by field automorphisms is a homomorphism $Go\mathrm{Aut}(L)$. Elements fixed by every group element are closed under addition, multiplication, additive inverses, and inversion of nonzero elements, so $L^G$ is a subfield.

Solved by gpt-5.6-sol high.