 Solution

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

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

The image contains

t

and

a^{2}

, hence also

t a^{2} t^{- 1} = a^{3}

. It therefore contains

a = a^{3} (a^{2})^{- 1}

, so it contains both generators of

S

. More explicitly,

θ (t a t^{- 1} a^{- 1}) = a, θ (t) = t,

which proves surjectivity.

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