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Question Number 193921 by Mastermind last updated on 23/Jun/23
Show that the kernel of a group homomorhism  θ : G → H is a normal subgroup.  Hint: Check the existence of the combination  g^(−1) kg in the kernel.
$$\mathrm{Show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{kernel}\:\mathrm{of}\:\mathrm{a}\:\mathrm{group}\:\mathrm{homomorhism} \\ $$$$\theta\::\:\mathrm{G}\:\rightarrow\:\mathrm{H}\:\mathrm{is}\:\mathrm{a}\:\mathrm{normal}\:\mathrm{subgroup}. \\ $$$$\mathrm{Hint}:\:\mathrm{Check}\:\mathrm{the}\:\mathrm{existence}\:\mathrm{of}\:\mathrm{the}\:\mathrm{combination} \\ $$$$\mathrm{g}^{−\mathrm{1}} \mathrm{kg}\:\mathrm{in}\:\mathrm{the}\:\mathrm{kernel}. \\ $$

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