  Let Gamma be an S-arithmetic subgroup of a solvable algebraic group G over an
algebraic number field F, such that the finite set S contains at least one
place that is nonarchimedean. We construct a certain group H, such that if L is
any local field and alpha is any homomorphism from Gamma to GL(n,L), then alpha
virtually extends (modulo a bounded error) to a continuous homomorphism defined
on some finite-index subgroup of H. In the special case where F is the field of
rational numbers, the real-rank of G is 0, and Gamma is Zariski-dense in G, we
may let H = G_S.
  We also point out a generalization that does not require G to be solvable.
