Timeline for p-groups as Sylow subgroups
Current License: CC BY-SA 2.5
17 events
| when toggle format | what | by | license | comment | |
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| Apr 29, 2011 at 9:32 | answer | added | Geoff Robinson | timeline score: 2 | |
| Feb 12, 2011 at 5:51 | vote | accept | Soluble | ||
| Feb 9, 2011 at 4:15 | history | edited | Soluble | CC BY-SA 2.5 |
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| Feb 7, 2011 at 21:01 | comment | added | Pete L. Clark | I clearly went too far in my second assertion, which I have now deleted (I hope that will not be confusing, but there is no doubt that it was wrong, so it doesn't seem to help the discussion to keep it there). Thanks, Charles, for pointing out that every finite p-group can be embedded in a Sylow p-subgroup of a symmetric group. | |
| Feb 7, 2011 at 20:44 | comment | added | Torsten Ekedahl | Oops, I kind of assumed that $q$ was a power of $p$ but I see that that is not a condition. | |
| Feb 7, 2011 at 18:43 | answer | added | Frieder Ladisch | timeline score: 4 | |
| Feb 7, 2011 at 18:10 | history | edited | Jim Humphreys | CC BY-SA 2.5 |
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| Feb 7, 2011 at 18:02 | answer | added | Jim Humphreys | timeline score: 2 | |
| Feb 7, 2011 at 15:16 | comment | added | Someone | @Torsten Ekedahl: Isn't $\mathrm{Z}_{49}$ a $7$-Sylow of $\mathrm{SL}_2(\mathbb{F}_{197})$? | |
| Feb 7, 2011 at 14:59 | comment | added | Torsten Ekedahl | I think a cyclic group of order $p^2$ is not Sylow $p$-group of any of the groups in question (and other similar ones). I agree with the feeling that most $p$-groups are not of that form. | |
| Feb 7, 2011 at 14:58 | answer | added | Joe Shmo | timeline score: 0 | |
| Feb 7, 2011 at 14:34 | comment | added | Jim Humphreys | I share Pete's view, though it would take some searching of the vast literature on finite simple groups to document the answer clearly. For instance, the third part of the ongoing AMS series of books by Gorenstein-Lyons-Solomon collects a large amount of information about the Sylow structure of finite groups of Lie type. | |
| Feb 7, 2011 at 14:30 | answer | added | Chris Godsil | timeline score: 11 | |
| Feb 7, 2011 at 14:11 | comment | added | Soluble | @Charles thats right... | |
| Feb 7, 2011 at 14:09 | comment | added | Charles Matthews | Obviously enough, after Cayley's theorem, any p-group is isomorphic with a subgroup of the Sylow p-subgroup of a symmetric group? | |
| Feb 7, 2011 at 14:02 | comment | added | Pete L. Clark | I'm pretty confident that the answer is no: this would make the set of finite $p$-groups much simpler than it actually is. One reasonable strategy for proving this would be a counting approach: write down an upper bound for the number of $p$-groups appearing as Sylow $p$-subgroups of one of these four families of groups, and then compare this to a lower bound for the number of isomorphism classes of $p$-groups of given order. I would expect the second quantity to be much larger than the first. | |
| Feb 7, 2011 at 13:49 | history | asked | Soluble | CC BY-SA 2.5 |