Hw8 Problem 7

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Problem 7

Let $G$ be a group with $|G|=pq$, where $p$ and $q$ are prime. Prove that every proper subgroup of $G$ is cyclic.


The possible orders for a proper subgroup would be $p, q$ and $1$. $p$ and $q$ are prime, meaning every subgroup of order $p$ & $q$ is cyclic, and any group of order $1$ is cyclic, so any proper subgroup of $G$ is cyclic.

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