Timeline for Structure of the group generated by two specific symplectic matrices
Current License: CC BY-SA 3.0
3 events
| when toggle format | what | by | license | comment | |
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| Nov 4, 2015 at 8:55 | history | edited | Geoff Robinson | CC BY-SA 3.0 |
Amended slightly
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| Nov 3, 2015 at 14:05 | comment | added | Matheus | You're right that this would help if one can figure out what is $p(K_q)$ (or something like it). Indeed, a simple-minded way to prove $H=<A,B>$ has infinite index is to find $g\in Sp(4,\mathbb{Z})$ of infinite order so that $\{g^n: n\in\mathbb{N}\}$ is disjoint from $H$, and, for this sake, I tried to play with some elements $g_0$ whose reduction mod 2 doesn't belong to the reduction mod 2 of $H$ (which is isomorphic to the alternate group inside $Sp(4,\mathbb{F}_2)\sim S_6$ if I'm not mistaken), but I got stuck since I could not figure out how to prove that $g_0^{2n}\notin H$ for all $n>0$. | |
| Nov 3, 2015 at 1:09 | history | answered | Geoff Robinson | CC BY-SA 3.0 |