Timeline for Galois Groups of a family of polynomials
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 3, 2014 at 14:25 | comment | added | fherzig | I only know how to prove Lemma 1 when $m = 1$ and $E/\mathbb{Q}_l$ is totally ramified. This is all that is needed. How is it proved in general (if it is true)? | |
| Apr 1, 2014 at 21:48 | comment | added | fherzig | I believe the standard result of Jordan that you refer to assumes that the action is primitive on $l-2$ points (and trivial on the rest), which is not guaranteed by an $(l-2)$-cycle, unless $l-2$ is prime. However, since $l-2 < (p-1)/2$ a theorem of Marggraff (1889, see Dixon-Mortimer's GTM 7.4B) shows that $G$ nevertheless contains $A_n$. So I guess this means CFSG is not actually necessary! | |
| Mar 3, 2011 at 5:24 | vote | accept | Victor Miller | ||
| Nov 11, 2010 at 20:48 | comment | added | Victor Miller | I had Magma calculate the galois group for $p=127$ (so all the non-$p$ ramification would be at 2) but it was still the full symmetric group. | |
| Nov 9, 2010 at 18:29 | comment | added | Victor Miller | Here's some speculation: If $g_n(x) = x^{n-1} f_n(1/x)$ then $x g_n(x)$ is a truncated version of $\log(1-x)$. Is there a connection with Coleman's (and Schur's) truncated exponential polynomials? | |
| Nov 9, 2010 at 14:04 | comment | added | Victor Miller | Terrific! It's amusing that we need CFSG. | |
| Nov 9, 2010 at 6:36 | history | answered | user631 | CC BY-SA 2.5 |