Does exist an example of a Galois extension $L/K$ such that $\text{Gal}(L/K)\cong \mathbb Z$?
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2In other words, there is no such extension. – Mariano Suárez-Álvarez Feb 11 '16 at 16:35
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Might as well move this to an answer, even though it's only one sentence. – anomaly Feb 11 '16 at 16:36
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Related: http://math.stackexchange.com/questions/1871485 – Watson Feb 03 '17 at 10:35
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The Galois group of a field extension $L/K$ is profinite, which $\mathbb{Z}$ is not.
anomaly
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