On isomorphism classes of Zariski dense subgroups of semisimple algebraic groups with isomorphic \(p\)-adic closures (Q1848133)

The author states a result saying that there is only a finite number of isomorphism classes of groups as stated in the title assuming that the groups involved are ``big'' which basically means that they are closed in the congruence topology. The idea of proof is taken from papers of Grunewald, Pickel and Segal, in particular [\textit{F. J. Grunewald, P. F. Pickel} and \textit{D. Segal}, Ann. Math. (2) 111, 155--195 (1980; Zbl 0431.20033)]. The author gives an outline of proof.