Timeline for Finite groups whose Carter subgroups are the Sylow 2-Subgroups
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 18 at 12:06 | comment | added | Geoff Robinson | There is no doubt that it is pretty hopeless to classify $2$-groups of a given $2$-power order, and while the question allows these, it may be that the intended spirit of the question is less concerned about $2$-groups. A finite group $G$ has a self-normalizing Sylow $2$-subgroup if and only if $G/O_{2}(G)$ has that property. So it might be more instructive to consider finite groups $G$ with a self-normalizing Sylow $2$-subgroup and with $O_{2}(G) = 1.$ | |
| Nov 18, 2016 at 18:53 | comment | added | zibadawa timmy | Almost all of those groups are the groups of order 512, though, which is a potentially misleading result. I don't think it makes sense to apply the question at hand to p-groups. It's trivial in those cases. | |
| Nov 18, 2016 at 18:35 | comment | added | maryam | Thanks. I think this number is rather amazing, since it is possible to exclude all p-groups of order less than 768. | |
| Nov 18, 2016 at 18:21 | vote | accept | maryam | ||
| Nov 18, 2016 at 17:01 | history | answered | Stefan Kohl♦ | CC BY-SA 3.0 |