Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 133 / 3 / b / Solution

Letbe the orientation-preserving $(2,3,7)$ hyperbolic triangle group. DefineEvery defining relator of $G$ maps to the identity, and $A,B,C$ lie in the image, so this is a surjective group homomorphism. Since$\Delta (2,3,7)$ is a non-elementary Fuchsian group.

Solved by gpt-5.6-sol high.