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If $\Lambda \cap U$ is Zariski-dense in $U$, then $\Lambda$ contains $U(k\mathbb Z)$ for some $k ≥ 1$?
If $G$ is a $\mathbb Q$-defined subgroup of $\operatorname{GL}_n(\mathbb C)$, $\Lambda$ is a subgroup of $G(\mathbb Z)$, and $U$ is a unipotent subgroup of $G(\mathbb C)$ such that $\Lambda \cap U$ is ...
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Automorphisms of products of $GL_n(\mathbb{Z})$ 's
It is a Theorem of Hua y Reiner (1951) that the group or outer automorphisms $Out(GL_n(\mathbb{Z}))$ is either isomorphic to $\mathbb{Z}/2$, if $n$ odd or $n=2$, or to $\mathbb{Z}/2 \times \mathbb{Z}/...
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