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Oct 3, 2019 at 16:37 answer added Algebrus timeline score: 1
Oct 3, 2019 at 11:01 vote accept Algebrus
Oct 3, 2019 at 8:24 answer added Aurel timeline score: 3
Oct 3, 2019 at 7:48 history edited Algebrus
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Oct 3, 2019 at 4:49 history edited Algebrus CC BY-SA 4.0
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Oct 3, 2019 at 4:41 comment added KConrad The example that I describe in an answer at mathoverflow.net/questions/21247/… does not directly address your question but it does show that the way a ramified prime number factors in $\mathcal O_K$ need not correspond to the way some element of the Galois group of the Galois closure of $K$ over $\mathbf Q$ permutes a primitive root of $K/\mathbf Q$ and its $\mathbf Q$-conjugates. Because of that phenomenon, I would not be surprised if your question has a negative answer.
Oct 3, 2019 at 3:04 history edited Algebrus CC BY-SA 4.0
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Oct 2, 2019 at 16:34 history asked Algebrus CC BY-SA 4.0