We consider solvable Lie groups which are isomorphic to unimodulariza-tions of products of affine groups. It is shown that a lattice of such a Lie group is determined,up to commensurability, by a totally real algebraic number field. We also show that the outerautomorphism group of the lattice is represented faithfully in the automorphism group of thenumber field. As an application, we obtain a classification of codimension one, volume pre-serving, locally free actions of products of affine groups.
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