Timeline for A question about finite groups.
Current License: CC BY-SA 2.5
4 events
| when toggle format | what | by | license | comment | |
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| Nov 14, 2010 at 18:08 | comment | added | Andrei Moroianu | Well, Derek's argument appears simpler to me, though. | |
| Nov 14, 2010 at 18:04 | comment | added | Alex B. | Actually, Tim's second argument about the vanishing of $H^2$ is independent of Schur-Zassenhaus and I don't think you can hope for anything simpler: the hypothesis that the order of your subgroup is co-prime to its index is crucial, because otherwise the result would be false in general. Since you asked whether $H^2$ vanished, it doesn't really get much simpler than just saying "yes, because it is killed by restriction-corestriction, which is multiplication by $2k+1$, and by 2". | |
| Nov 14, 2010 at 17:21 | comment | added | Andrei Moroianu | Thanks, Tim; I have found some more references about the S-Z theorem here: math.uconn.edu/~kconrad/blurbs/grouptheory/schurzass.pdf I wonder, however, if there is some simple argument in this particular case, since I have the impression that one burns the house to fright the mouse away (this is the english equivalent I have found for the french expression 'tuer une mouche avec un canon'). | |
| Nov 14, 2010 at 15:08 | history | answered | Tim Dokchitser | CC BY-SA 2.5 |