2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/71355Let A = Z[c], where c is an irrational number whose square is rational, or let A = Z[1/r], where r > 1 is a square-free natural number. We show that no finite-index subgroup of SL(2,A) 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 subgroup of G is left orderable. Our proofs are based on the fact, proved by B.Liehl, that every element of SL(2,A) is a product of a bounded number of elementary matrices.4 pages, no figures; new title, abstract and introduction to reflect improved conclusions in the nonarchimedean caseGroup Theory20F60; 06F15, 11F06, 20F65, 22E40, 57S25text