
Journal of Lie Theory 18 (2008), No. 3, 733746 Copyright Heldermann Verlag 2008 The Bohr Topology of Discrete Nonabelian Groups Salvador Hernández Dep. de Matemáticas, Area CientíficoTécnica, Universidad Jaume I, 8029  AP Castellón, Spain hernande@mat.uji.es 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) 1540]; if G is a countable FC group, then the topology that the commutator subgroup [G,G] inherits from G^{#} is residually finite and metrizable. Keywords: Discrete group, finitely generated group, free nonabelian group, finite conjugacy group, dually embedded group, Bohr compactification, Bohr topology. MSC: 22D35, 43A40; 22D05, 22D10, 54H11 [ Fulltextpdf (223 KB)] for subscribers only. 