Does exist an example of a Galois extension $L/K$ such that $\text{Gal}(L/K)\cong \mathbb Z$?
Thank you.
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2$\begingroup$ In other words, there is no such extension. $\endgroup$– Mariano Suárez-ÁlvarezFeb 11, 2016 at 16:35
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$\begingroup$ Might as well move this to an answer, even though it's only one sentence. $\endgroup$– anomalyFeb 11, 2016 at 16:36
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$\begingroup$ Related: math.stackexchange.com/questions/1871485 $\endgroup$– WatsonFeb 3, 2017 at 10:35
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1 Answer
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The Galois group of a field extension $L/K$ is profinite, which $\mathbb{Z}$ is not.
