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Question

Let $G$ be an Abelian group and $H = \{ x \in G | | x |$ is 1 or even $\} .$ Give an example to show that $H$ need not be a subgroup of $G .$

Solution

VerifiedIf $G=\mathbb Z_6=\{0,1,2,3,4,5\}$ then $H=\{0,1,3,5\}$, which is not a subgroup since $1+1=2\not\in H$.

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