Journal of Lie Theory

We look at finitely generated Bohr groups G^#, i.e., groups G equipped with the topology inherited from their Bohr compactification bG. Among other things, the following results are proved: every finitely generated group without free nonabelian subgroups either contains nontrivial convergent sequences in G^# or is a finite extension of an abelian group; every group containing the free nonabelian group with two generators does not have the extension property for finite dimensional representations, therefore, it does not belong to the class D introduced by D. Poguntke ["Zwei Klassen lokalkompakter maximal fastperiodischer Gruppen, Monatsh. Math. 81 (1976) 15--40]; if G is a countable FC group, then the topology that the commutator subgroup [G,G] inherits from G^# is residually finite and metrizable.