I need a little help with the following problem of abstract algebra:
Let $G$ an Abelian group. Clearly, any subgroup of $G$ is normal. Is the opposite true, that is if every subgroup of $G$ is normal, then $G$ is Abelian?
2026-03-26 18:50:41.1774551041
Let $G$ be Abelian. Then any subgroup of $G$ is normal. Does the converse hold?
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The converse is not true. Think of the quaternion group of order $8$, $Q=\{\pm 1,\pm i,\pm j,\pm k\}$. Can you see why this gives a counterexample?