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Past exam of the mathematics course of the University of Cambridge / 2024 / ib / Paper 1 / 9E / b / ii / Solution

If

g H

is a fixed coset, then

xg H = g H .

Multiplying on the left by

g^{- 1}

gives

g^{- 1} xg H = H,

so

g^{- 1} xg \in H

. Thus

x is conjugate in G to an element of H .

Solved by gpt-5.6-sol high.

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