Timeline for Finite group ${\rm Sp}_4({\Bbb F}_3)$: involutions coming from a 4-dimensional complex representation
Current License: CC BY-SA 4.0
15 events
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| May 18, 2020 at 17:05 | history | edited | Mikhail Borovoi | CC BY-SA 4.0 |
Typo in a formula corrected
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| May 18, 2020 at 12:38 | vote | accept | Mikhail Borovoi | ||
| May 18, 2020 at 12:38 | comment | added | Mikhail Borovoi | Many thanks indeed! | |
| May 18, 2020 at 12:32 | comment | added | Derek Holt | Sorry, that was a typo. I have given an example of an element from the second class. | |
| May 18, 2020 at 12:32 | history | edited | Derek Holt | CC BY-SA 4.0 |
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| May 18, 2020 at 12:26 | comment | added | Mikhail Borovoi | ``$G_-$ is not a group.'' Good! However, you write: " We can take $H={\rm Sp}(4,3)$ to be the group $\{ A \in {\rm GL}(4,3) \mid AFA^{\mathsf T} = -F\}$". I was a bit puzzled.... | |
| May 18, 2020 at 12:19 | comment | added | Mikhail Borovoi | Concerning Question 2: Of course you are right! I used bad notation. By ${\rm PSp}_4(\Bbb F_3)$ I meant ${\rm PCSp}(4,3)$. | |
| May 18, 2020 at 12:18 | comment | added | Derek Holt | $G_-$ is not a group. It is a coset of $G_+ = {\rm Sp}(4,3)$ in the larger group ${\rm CSp}(4,3)$. | |
| May 18, 2020 at 11:51 | comment | added | Mikhail Borovoi | Concerning Question 3. You mention two conjugacy classes of involutary outer automorphisms of $H$, one of which is induces by the matrix $C$. What is the second conjugacy class? | |
| May 18, 2020 at 11:47 | comment | added | Mikhail Borovoi | Many thanks! A stupid question: I know the definition of the symplectic group ${\rm Sp}(4,3):={\rm Sp}_4( {\Bbb F}_3)$ as the group $$G_+=\{ A \in {\rm GL}(4,3) \mid AFA^{\mathsf T} = F\}.$$ However, you take the group $$G_-=\{ A \in {\rm GL}(4,3) \mid AFA^{\mathsf T} = -F\}.$$ How can one define an isomorphism between $G_+$ and $G_-$? | |
| May 18, 2020 at 8:49 | history | edited | Derek Holt | CC BY-SA 4.0 |
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| May 18, 2020 at 8:32 | history | edited | Derek Holt | CC BY-SA 4.0 |
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| May 18, 2020 at 8:02 | comment | added | Derek Holt | @LSpice Thanks! "..e looking for". | |
| May 18, 2020 at 8:02 | history | edited | Derek Holt | CC BY-SA 4.0 |
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| May 18, 2020 at 7:46 | history | answered | Derek Holt | CC BY-SA 4.0 |