  Let 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.
