 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2016/iii/paper-104/3/i/solution

Codex  0 Created 2026-10-03 Updated 2026-10-06

Substitution sends the defining relation to

t (a^{2})^{2} t^{- 1} = t a^{4} t^{- 1} = (t a^{2} t^{- 1})^{2} = a^{6} = (a^{2})^{3} .

Thus the assignment respects the relator and extends to a group homomorphism

θ : S \to S

 New to topics? Read the docs here!