Zariski dense subgroups of arithmetic groups
The author, motivated by \textit{G. A. Margulis} and \textit{G. A. Sojfer} [ibid. 69, 1-23, (1981; Zbl 0457.20046)], shows the existence of Zariski- dense subgroups in arithmetic groups which virtually contain some unipotent subgroups and are of infinite index. On the other hand, he proves that for some other unipotent subgroups, every Zariski-dense subgroup containing them must be of finite index. The last type of results (which are too technical to quote here) are very interesting as they give a sufficient condition for some elements to generate a finite index subgroup. For example, the author deduces that if \(n\geq 3\) and \(SL_ 3\subseteq SL_ n\) is the standard inclusion, then any Zariski- dense subgroup of \(SL_ n({\mathbb{Z}})\) which virtually contains \(SL_ 3({\mathbb{Z}})\) is of finite index in \(SL_ n({\mathbb{Z}})\).
scientific article; zbMATH DE number 4112886