Timeline for Density of the conjugacy classes of the inertia groups in Galois group of $\mathbb{Q}$
Current License: CC BY-SA 4.0
3 events
| when toggle format | what | by | license | comment | |
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| Oct 14, 2022 at 15:19 | comment | added | Will Sawin | @Nobody I don't think I said that it was! It's not true for $S =\{253381\}$ since the extension generated by the roots of $x^5+ x+3$ is ramified only at that prime (since its discriminant is $253381$) and the inertia group consists of an element of order $2$ in the Galois group and the trivial element, but not every element in the Galois group has order $1$ or $2$. | |
| Oct 14, 2022 at 14:19 | comment | added | Nobody | Thanks so much for your counterexample! But why is it true when $S$ has only one element? | |
| Oct 14, 2022 at 13:33 | history | answered | Will Sawin | CC BY-SA 4.0 |