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Results tagged with arithmetic-groups
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user 21684
11
votes
Accepted
Subgroups of $SL_3(\mathbb{Z})$ that are finitely generated, Zariski-dense, infinite index, ...
Here is what's known about this question:
The problem is hard and requires new ideas. The situation in the $SL(4,Z)$ case is very different and the analogy is misleading.
$\Gamma=SL(3,Z)$ contains …
- 31.2k
4
votes
Is the group of integer points of ${\rm SO}(n,1)$ maximal?
Here is a proof for even $n$, I am not quite sure about odd $n$ since $G=SO(n,1)$ is not an adjoint group and weak approximation might fail in this case (I do not know enough about this, you would nee …
- 31.2k
2
votes
Accepted
Siegel set in SO(n,1) modulo integer points?
The number of cusps could be more than 1, see here, remark on page 294.
- 31.2k
5
votes
Zariski density of conjugates of subgroups by arithmetic subgroups?
Part (2) is also hopeless: If you look at the proof of the Tits' alternative, you see that every lattice $\Gamma$ in a semisimple Lie group will contain a "Schottky subgroup", which is a free subgroup …
- 31.2k