Is it true that an element of a group whose order divides the order a subgroup is an element of the subgroup – math.stackexchange.com

Is it true that an element of a group whose order divides the order a subgroup is an element of the subgroup – math.stackexchange.com

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Let $G$ be a group. Suppose that the order of $G$ is finite and that $H$ is a subgroup of $G$. Is it true that an element of $G$ whose order divides the order of $H$ is in $H$? Here is my attempt: ...

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