Given a field F, I know that if F is finite, then its group of units F* is cyclic. I'm trying to prove the converse: if F* is cyclic, then F is finite.(adsbygoogle = window.adsbygoogle || []).push({});

I have no idea where to start; I've tried a few things and they didn't get me anywhere. I know that if F is infinite and F* is cyclic, then F* is isomorphic toZ, but I can't figure out how that might form a contradiction.

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# Group of units of a field

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