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If OS is the ring of S-integers of an algebraic number field F, and OS has infinitely many units, we show that no finite-index subgroup of SL(2,OS) is left orderable. (Equivalently, these subgroups have no nontrivial orientation-preserving actions on the real line.) This implies that if G is an isotropic F-simple algebraic group over an algebraic number field F, then no nonarchimedean S-arithmetic...
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