Timeline for Automorphism of simple lie type groups
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Nov 29, 2014 at 5:18 | comment | added | Derek Holt | There must be lots of similar examples gotten by extending by the product of diagonal and field automorphisms of the same order. For example you could take $G$ to be an extension of ${\rm PSL}(3,7^3)$ by an element of order $3$. | |
| Nov 29, 2014 at 4:32 | comment | added | Hamid | @Nick, I edit base on your last comment. Exept $PSL_2(q)$ is there any counterexample? | |
| Nov 29, 2014 at 4:24 | history | edited | Hamid | CC BY-SA 3.0 |
added 17 characters in body
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| Nov 29, 2014 at 1:33 | comment | added | Nick Gill | One last comment: I presume you mean "generated by all inner and diagonal automorphisms of $S$ that lie in $G$", otherwise I'm not sure that the definition of $G_0$ makes sense. | |
| Nov 28, 2014 at 21:48 | comment | added | Nick Gill | Checking the atlas for $p=5$ implies that $y$ and $xy$ are not conjugate in that case. So there's one counterexample (with Def 2.5.13 of GLS3). | |
| Nov 28, 2014 at 21:47 | comment | added | Nick Gill | Possible counterexample: consider $S=PSL_2(p^2)$ for some odd prime $p$. Let $G$ be the group $\langle S, h\rangle$ where $h$ is the product of a diagonal automorphism $x$ and a field automorphism $y$ (both of order $2$). Depending on your definitions, this would be a counter-example so long as $y$ and $xy$ are not conjugate in $Aut(S)$. I guess they aren't but would need to check to be sure. | |
| Nov 28, 2014 at 21:42 | comment | added | Nick Gill | You probably need to define graph, field and graph-field automorphisms explicitly as there is no universal terminology. (For instance Gorenstein, Lyons & Solomon have two definitions of field and graph auts in their volume 3 - see Warning 2.5.2 of that book.) | |
| Nov 28, 2014 at 21:21 | history | asked | Hamid | CC BY-SA 3.0 |