Let $K,L$ over $Q$ be field extension of prime degrees. Prove if $[KL:Q]<[K:Q][L:Q]$, then the Galois closure of $K/Q$ is the Galois closure of $L/Q$.

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Monolithic Groups

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When a group homorphism must be $K$-linear

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Let $K,L$ over $Q$ be field extension of prime degrees. Prove if $[KL:Q]<[K:Q][L:Q]$, then the Galois closure of $K/Q$ is the Galois closure of $L/Q$.

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