 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-2-of-the-natural-sciences-course-of-the-university-of-cambridge/2022/paper-2/8/a/solution

The group order of a finite group is its number of elements,

∣ G ∣ = # G

H

is normal when conjugation by any group element leaves it unchanged:

g H g^{- 1} = H for every g \in G .

Equivalently, its left and right cosets agree:

g H = H g

for every

g

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