Isotropic nonarchimedean S-arithmetic groups are not left orderable Groupes S-arithmétiques non-archimédiens isotropes ne sont pas ordonnés à gauche
نویسنده
چکیده
If O is either Z[ √ r] or Z[1/r], where r > 1 is any square-free natural number, we show that no finite-index subgroup of SL(2,O) 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,O) is a product of a bounded number of elementary matrices.
منابع مشابه
Isotropic nonarchimedean S-arithmetic groups are not left orderable
If Os is the ring of S-integers of an algebraic number field F, and 0,s has infinitely many units, we show that no finiteindex 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-arithm...
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