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On arithmetic subgroups of simple algebraic groups. (English) Zbl 0594.20038
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 ${}\sp 3D\sb 4$ or ${}\sp 6D\sb 4$, 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.
Reviewer: A.M.Cohen
##### MSC:
 20G30 Linear algebraic groups over global fields and their integers 20E07 Subgroup theorems; subgroup growth 20H05 Unimodular groups, congruence subgroups (matrix groups)
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##### References:
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