Timeline for Number of imaginary quadratic field with its ideal class group has $\Bbb{Z}/2\Bbb{Z}$ as 2 part
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 6 at 8:09 | comment | added | David Loeffler | Yes, this is genus theory. | |
| Oct 4 at 23:43 | comment | added | Duality | Is your claim regarding $Cl_K[2]$ in your answer a direct consequence of the so-called genus theory? If there are any formal documents (such as papers published in journals or books) that state the claim about $Cl_K[2]$, would it be possible for you to provide their references? | |
| Jan 24 at 20:33 | vote | accept | Duality | ||
| Aug 4, 2023 at 8:14 | comment | added | David Loeffler | Please don't ask new questions in comments. | |
| Jul 18, 2023 at 9:20 | comment | added | David Loeffler | Yes, that's an obvious and well known corollary. | |
| Jul 17, 2023 at 17:09 | comment | added | Duality | Thanks to your result, I thought that we can prove there are infinitely many quadratic fields with odd class number. There are infinitely many $K$ such that $Cl_K[2]=1$. Thus $Cl_K$ is odd abelian group! | |
| Jul 16, 2023 at 15:14 | comment | added | David Loeffler | It's come up before on this site, see mathoverflow.net/questions/431499/… | |
| Jul 16, 2023 at 14:13 | comment | added | Duality | Thank you very much. I searched a lot, but I couldn't find any reference for the fact that $\# Cl_K[2]=2^{r-1}$. Could you please provide me with a reference for that? | |
| Jul 11, 2023 at 21:41 | comment | added | David Loeffler | @WillJagy I've added a clarification of exactly what I'm answering (since the title of the question, the first paragraph of the question, and the final paragraph are actually asking three distinct questions) | |
| Jul 11, 2023 at 21:40 | history | edited | David Loeffler | CC BY-SA 4.0 |
added 247 characters in body
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| Jul 11, 2023 at 9:51 | history | answered | David Loeffler | CC BY-SA 4.0 |