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Potentially compact Abelian groups. (Russian) Zbl 0704.22003

A group G is said to be potentially compact if, for every ultrafilter on G, there is a Hausdorff group topology on G such that the ultrafilter converges. A subgroup G of a topological group H is called a topological serving subgroup if, for every \(h\in H\), there is \(g\in G\) such that \([Cl<g+h>]\cap G=\{0\}\). Reduced p-groups and free groups of rank at least 2 are potentially compact, while free cyclic groups are not. In general, a group G is potentially compact iff it is a topological serving subgroup of its Bohr compactification. A periodic group is potentially compact iff G is reduced and the number of p-Sylow subgroups is finite.
Reviewer: D.L.Grant

MSC:

22A05 Structure of general topological groups
54D30 Compactness
54A20 Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.)
20K45 Topological methods for abelian groups
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