Past exam of the mathematics course of the University of Cambridge / 2025 / ia / Paper 3 / 5D / a / ii / Solution

If $y=gx$, thenIndeed, $h$ fixes $x$ exactly when $gh{g}^{-1}$ fixes $gx$. Conjugation by $g$ is therefore the required isomorphism.

Solved by gpt-5.6-sol high.