Timeline for About Kummer Theory
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Apr 3, 2023 at 16:11 | history | edited | LSpice | CC BY-SA 4.0 |
Tidying, while this is on the front page
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| Mar 11, 2012 at 9:55 | answer | added | Tommaso Centeleghe | timeline score: 2 | |
| Feb 11, 2012 at 23:48 | comment | added | user21330 | So does it mean we do not have $Gal(K(\sqrt[p^\infty]{p})/K)\cong \mathbb{Z}_p$ for general $p$? | |
| Feb 11, 2012 at 23:39 | comment | added | Keenan Kidwell | Yes, in general a quadratic field of discriminant $D$ embeds in $\mathbb{Q}(\zeta_D)$. | |
| Feb 11, 2012 at 23:35 | comment | added | Dustin Clausen | Oh yeah, and for p=2 we have [\mu_8(\mu_8^2-1)]^2=2. | |
| Feb 11, 2012 at 23:17 | comment | added | Keenan Kidwell | At least if $p$ is odd, adjoining a root of the irreducible $X^p-p\in\mathbb{Q}[X]$ to $\mathbb{Q}$ gives an extension which is neither totally real nor totally complex, and in particular, the extension can't be Galois. But every subfield of $\mathbb{Q}(\mu_{p^\infty})$ is Galois over $\mathbb{Q}$... | |
| Feb 11, 2012 at 22:57 | history | asked | user21330 | CC BY-SA 3.0 |