On arithmetic subgroups of simple algebraic groups (Q1076806)

Let k be a number field, and G an absolutely almost simple algebraic group defined over k which is either of classical type distinct from \({}^ 3D_ 4\) or \({}^ 6D_ 4\), or split, and in which every maximal k-split torus has rank at least 2. The main result of the paper is that a subgroup of G(k) is full (i.e., for each maximal k-split torus of G, every root subgroup with respect to this torus meets H nontrivially) if and only if it contains an arithmetic subgroup.