Can the pre-image (under homomorphism) of a subgroup be empty? – math.stackexchange.com

Can the pre-image (under homomorphism) of a subgroup be empty? – math.stackexchange.com

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I'm asked to prove that if $E \leq H, \varphi^{-1}(E) \leq G$ where $\varphi: G \rightarrow H$ is an homomorphism. I can show that $\varphi^{-1}(E)$ satisfies the group condition of $\forall x, y \in ...

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