Timeline for Group action w.r.t. non-split extension group of the form $2^8\mathbin.(2^7\mathbin:\operatorname{Sp}(6,2))$
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 29, 2021 at 7:50 | vote | accept | Isaac | ||
| Nov 20, 2019 at 20:46 | comment | added | Isaac | I am still waiting on a response to the last question. | |
| Nov 10, 2019 at 6:18 | comment | added | Isaac | The action of $2^7:Sp (6,2) $ ( constructed as a 8×8 matrix group within Sp (8,2)) on $2^8$ forms 4 orbits of elements of $2^8$. I checked it with GAP. What do we call this action? | |
| Nov 9, 2019 at 22:51 | comment | added | Derek Holt | No, as I said , that subgroup is the stabilizer of a vector. It also stabilizes a $7$-dimensional subspace (which is the space orthogonal to the fixed vector under the symplectic form), and the subgroup ${\rm Sp}(6,2)$ acts in its natural action on the $6$-dimensional quotient of the $7$- by the $1$-dimensional fixed spaces. | |
| Nov 9, 2019 at 16:14 | comment | added | Isaac | So we can then consider $2^8$ as the vector space V(8,2) where upon $2^7:$Sp (6,2) acts as an eight dimensional matrix group over GF (2). I suppose this action is not irreducible. | |
| Nov 9, 2019 at 13:49 | history | edited | Derek Holt | CC BY-SA 4.0 |
added 1 character in body
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| Nov 9, 2019 at 13:12 | history | answered | Derek Holt | CC BY-SA 4.0 |