Timeline for Conjugacy classes in lie type group
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Dec 1, 2014 at 22:39 | comment | added | Nick Gill | For field automorphisms: the definition of a field automorphism of a Chevalley group is that it is an $Aut(S)$ conjugate of en element of $\Phi_S$ where $\Phi_S$ is the cyclic subgroup of "entry-by-entry automorphisms". So the conjugacy structure is a triviality. For Steinberg groups and the others the definitions are similar (see Def. 2.5.13 of GLS3). | |
| Dec 1, 2014 at 22:35 | comment | added | Nick Gill | There are loads of references for this sort of thing - for $PSL_n(q)$ you can use rational forms, for the other classical groups there are variations on rational forms due to MacDonald and also to Wall. For groups of Lie type in full generality I would go to Carter's Finite groups of Lie type. The ATLAS is also very helpful for individual small groups. | |
| Nov 30, 2014 at 18:51 | comment | added | Geoff Robinson | As to 2, there are certainly field automorphisms of order $p$ for some values of $q.$ For example when $q = p^{p},$ the automorphism $a \to a^{p}$ of ${\rm GF}(q)$ has order $p.$ | |
| Nov 30, 2014 at 18:50 | review | First posts | |||
| Nov 30, 2014 at 18:51 | |||||
| Nov 30, 2014 at 18:48 | history | asked | maryam | CC BY-SA 3.0 |