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Journal of Lie Theory 18 (2008), No. 3, 733--746
Copyright Heldermann Verlag 2008

The Bohr Topology of Discrete Nonabelian Groups

Salvador Hernández
Dep. de Matemáticas, Area Científico-Técnica, Universidad Jaume I, 8029 - AP Castellón, Spain

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.

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

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