Timeline for Galois groups of CM fields
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 19, 2013 at 18:13 | vote | accept | cmfield | ||
| Mar 19, 2013 at 14:14 | answer | added | Venkataramana | timeline score: 2 | |
| Mar 19, 2013 at 10:17 | comment | added | cmfield | Sure! That's what I meant by "If the extension is not Galois..." So in degree 4 is it true that if the K is not abelian, then the Galois group is $D_4$? What about degree 6? | |
| Mar 19, 2013 at 10:14 | comment | added | Venkataramana | The Galois group is of the Galois closure of $K$. | |
| Mar 19, 2013 at 10:13 | comment | added | Venkataramana | When you take $K_0={\mathbb Q}({\sqrt 2}$ and $K=K_0[X]/(X^2+{\sqrt 2})$, it is clear that $[K:{\mathbb Q}]=4$ but it is not Galois. The Galois group is not abelian but is of order $8$. | |
| Mar 19, 2013 at 9:46 | comment | added | cmfield | Could you elaborate more on your last sentence "CM points will define CM fields with dihedral Galois group"? Thanks! | |
| Mar 19, 2013 at 9:43 | comment | added | cmfield | Why should a degree four CM field be Galois? | |
| Mar 19, 2013 at 9:12 | history | asked | cmfield | CC BY-SA 3.0 |