Timeline for Why is every quadratic subfield of a Galois extension of the rationals with the quaternions as Galois group real?
Current License: CC BY-SA 2.5
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| Sep 16, 2010 at 10:43 | comment | added | Robin Chapman | There's less to the problem than this. Embed $L$ in $\mathbb{C}$ and consider the complex conjugation map $c$. Then $c$ restricts to an automorphism of $L$ (why?) and so corresponds to one of the elements of the group $Q$. Which elements of $Q$ are possible? | |
| Sep 16, 2010 at 10:28 | comment | added | Alex B. | That rule of thumb sounds like it could be very close to the truth and I think I will adopt it. I guess I will leave this one, since your average undergraduate doesn't usually know Dirichlet's unit theorem (not the undergrads I know, anyway), so probably wouldn't get away with using it in a solution. | |
| Sep 16, 2010 at 10:22 | comment | added | Kevin Buzzard | Hi Alex. You just can't tell with these problems. It's a perfectly valid "idle question" but also a perfectly valid homework problem. Here's my rule of thumb: if the questioner has a reputation of 1 then I assume it's homework, and if it's a regular I assume it's an idle question. So you can see why I said what I said---the questioner has no prior history. But other people think differently. | |
| Sep 16, 2010 at 10:21 | comment | added | Alex B. | Just saw Kevin's comment. Maybe I should withdraw my post. What do you think? On the other hand, if it's homework, I doubt that this is the sort of answer the lecturer is looking for. | |
| Sep 16, 2010 at 10:18 | history | answered | Alex B. | CC BY-SA 2.5 |