 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-2-of-the-natural-sciences-course-of-the-university-of-cambridge/2022/paper-2/9/a/solution

For

g \in G

, the left coset of

H

represented by

g

g H = {g h : h \in H} .

It is a subset of

G

obtained by multiplying every element of

H

on the left by the same group element. The identity representative gives

eH = H

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