Timeline for p-groups as Sylow subgroups
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
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| Feb 12, 2011 at 5:51 | vote | accept | Soluble | ||
| Feb 9, 2011 at 22:57 | comment | added | Jim Humphreys |
@Someone: I agree that my offhand comment went too far. Of course, embedding a $p$-group in some huge Sylow $p$-subgroup won't tell you much about the smaller group.
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| Feb 8, 2011 at 15:52 | comment | added | Someone |
@Jim: Yes, I agree. My comment referred to your "For these families it doesn't even seem plausible to me that one can embed an arbitrary $p$-group into such a Sylow subgroup over a large enough field of characteristic $p$."
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| Feb 8, 2011 at 14:21 | comment | added | Jim Humphreys |
@Someone: I guess this amounts to embedding $P$ into a symmetric group and then embedding this symmetric group into a finite general linear group. What can all of this tell you about $P$? Anyway the original question asks for $P$ to be embedded into one of the listed groups as a Sylow $p$-subgroup.
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| Feb 8, 2011 at 9:16 | comment | added | Someone | You should be able to embed any finite $p$-group $P$ into $\mathrm{GL}_n(\mathbb{F}_p)$ for $n := |P|$ by letting $P$ act regularly on the base (or take any other faithful action). | |
| Feb 7, 2011 at 18:02 | history | answered | Jim Humphreys | CC BY-SA 2.5 |