Question
If $N$ is a normal subgroup of $G$ and $|G / N|=m$, show that $x^{m} \in N$ for all $x$ in $G$.
Step 1
Since $|G/N| = m$, we know that there are $m$ distinct cosets of $N$ in $G$. Let $x \in G$. Then the coset $xN$ is one of these $m$ cosets. Show more…
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