Index-two subgroup is normal

H \leq G

of index two is normal: the two left cosets and the two right cosets are both

H

and its complement, so they agree.

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Past exam of the mathematics course of the University of Cambridge / 2011 / ia / Paper 3 / 8D / a / Solution
Past exam of the mathematics course of the University of Cambridge / 2020 / ii / Paper 3 / 18G / a / Solution
Past exam of the mathematics course of the University of Cambridge / 2023 / ii / Paper 2 / 21G / Solution

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