Question
Let $H$ be a subgroup of a finite group $G$. Suppose that $g$ belongs to $G$ and $n$ is the smallest positive integer such that $g^{n} \in H$. Prove that $n$ divides $|g|$.
Step 1
Since $H$ is a subgroup of $G$, we know that $H$ is closed under the group operation and contains the identity element $e$. Show more…
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