Timeline for What is the smallest group not known to be a Galois group over $\mathbb{Q}$?
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| Aug 24, 2023 at 8:46 | comment | added | Jianing Song | For one's information, it seems that the groups you are talking about are $\operatorname{SmallGroup}(672,1044)$ and $\operatorname{SmallGroup}(672,1045)$ (from the link Groups of order 672). | |
| Mar 22, 2023 at 1:10 | comment | added | Joachim König | These groups are no longer open, as observed by Malle in Section 12 of mathematik.uni-kl.de/~malle/download/pargal.pdf , the reason essentially being the existence of a local-global principle for central embedding problems (together with the availability of sufficiently nice $PGL_2(7)$ extensions). Which (together with all other pre-existing evidence) might make the author of that paper the right person to ask. | |
| Mar 21, 2023 at 22:59 | history | answered | Pace Nielsen | CC BY-SA 4.0 |