Consider field extensions of the form Q(u) where Q is the field of rational numbers and [itex]u=e^{\frac{2\pi i}{n}}[/itex], the principal nth root of unity. For what values of n is the Galois group of Q(u) over Q cyclic? It seems to at least hold when n is prime or twice an odd prime, but what else?(adsbygoogle = window.adsbygoogle || []).push({});

Any help would be greatly appreciated.

Thank You in Advance.

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# Galois Groups of Extensions by Roots of Unity

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