In a recent paper, K. B. Lee introduced the notion of an infra-solvmanifold of type (R). These manifolds are completely determined by their fundamental group Π. Such a Π is a finite extension of a lattice Γ of a solvable Lie group of type (R) and this lattice Γ is called the translational part of Π.

Having fixed an abstract group Π occurring as the fundamental group of an infra-solvmanifold of type (R), it seems to be hard to describe, in a formal algebraic language, which subgroup of Π is the translational part. In his paper Lee formulated a conjecture which would solve this problem, however, we show that this conjecture fails. Nevertheless, by defining a concept of eigenvalues for automorphisms of certain solvable groups (both Lie groups and discrete groups), we are able to prove a new theorem, characterizing completely the translational part of the fundamental group of an infra-solvmanifold of type (R).