I'm doing a lot of Galois Theory lately. Now I'm more and more into $p$-adic fields. My goal is to choose an irreducible polynomial of degree $3$ over $\mathbb{Q}_2$ and $\mathbb{Q}_3$ such that you obtain $A_3$ or $S_3$ as its Galois group. Is there an easy way to find such a polynomial? Could you shortly explain by an example?
2026-04-03 11:42:36.1775216556
How to obtain $\operatorname{Gal}(f\mid \mathbb{Q}_3)=A_3$ or $S_3$?
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