Geodesic
The Bohr Topology of Discrete Nonabelian Groups
Journal of Lie theory, Tome 18 (2008) no. 3, pp. 733-746
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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.
Classification : 22D35, 43A40, 22D05, 22D10, 54H11
Mots-clés : Discrete group, finitely generated group, free nonabelian group, finite conjugacy group, dually embedded group, Bohr compactification, Bohr topology 
@article{JLT_2008_18_3_JLT_2008_18_3_a15,
     author = {S. Hern\'andez},
     title = {The {Bohr} {Topology} of {Discrete} {Nonabelian} {Groups}},
     journal = {Journal of Lie theory},
     pages = {733--746},
     year = {2008},
     volume = {18},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JLT_2008_18_3_JLT_2008_18_3_a15/}
}
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S. Hernández. The Bohr Topology of Discrete Nonabelian Groups. Journal of Lie theory, Tome 18 (2008) no. 3, pp. 733-746. http://geodesic.mathdoc.fr/item/JLT_2008_18_3_JLT_2008_18_3_a15/