Galois group isomorphic to $\mathbb Z$

Question

Does exist an example of a Galois extension $L/K$ such that $\text{Gal}(L/K)\cong \mathbb Z$?

Thank you.

Might as well move this to an answer, even though it's only one sentence. — anomaly, Feb 11 '16 at 16:36

score 6 · Accepted Answer · answered Feb 11 '16 at 16:35

6

The Galois group of a field extension $L/K$ is profinite, which $\mathbb{Z}$ is not.

answered Feb 11 '16 at 16:35

anomaly

1 Answers1