Timeline for Soluble subgroups of 8-dimensional orthogonal groups over GF(4) transitive on nondegenerate 1-subspaces
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Jul 18, 2013 at 14:30 | comment | added | Binzhou Xia | @DerekHolt:$N_G((PSL_2(16)\times PSL_2(16)).2^2)$ is maximal in $G$ if and only if $G=L$ or $L.2$, so by your computation for $\Gamma O_8^+(4)$, my statement holds. Thank you so much! | |
| Jul 18, 2013 at 10:58 | comment | added | Binzhou Xia | @DerekHolt: What if $G$ contains a graph automorphism? | |
| Jul 16, 2013 at 2:38 | comment | added | Binzhou Xia | @DerekHolt:By THEOREM A of Liebeck, Praeger and Saxl, The maximal factorizatins of the finite simple groups and their automorphism groups, I would be able to show that if $H$ is not contained in any maximal parabolic subgroup then $H\cap L$ is contained in $(L_2(16)\times L_2(16)).2^2$ (as $C_2$ or $C_3$ subgroup of $L$). Does this help? | |
| Jul 15, 2013 at 8:52 | comment | added | Derek Holt | I did some computer calculations in Magma, and I found that the only soluble subgroups of $\Gamma O^+_8(4)$ that were transitive on the 16320 nondegenerate 1-subspaces had nontrivial normal 2-subgroups, so the answer would appear to be yes. | |
| Jul 14, 2013 at 14:37 | history | asked | Binzhou Xia | CC BY-SA 3.0 |