Geodesic
The Bohr Topology of Discrete Nonabelian Groups
Journal of Lie Theory, Tome 18 (2008) no. 3, pp. 733-746

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Zbl

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 
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/JOLT_2008_18_3_a15/
@article{JOLT_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},
     zbl = {1205.22006},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2008_18_3_a15/}
}
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