Which infinite abelian groups admit an almost maximally almost-periodic group topology?
نویسندگان
چکیده
منابع مشابه
2 00 8 Which infinite abelian torsion groups admit an almost maximally almost - periodic group topology ? *
A topological group G is said to be almost maximally almost-periodic if its von Neumann radical n(G) is non-trivial, but finite. In this paper, we prove that (a) every countably infinite abelian torsion group, (b) every abelian torsion group of cardinality greater than continuum, and (c) every (non-trivial) divisible abelian torsion group admits a (Hausdorff) almost maximally almost-periodic gr...
متن کاملWhich Infinite Abelian Groups Admit an Almost Maximally Almost-periodic Group Topology?
A topological group G is said to be almost maximally almost-periodic if its von Neumann radical n(G) is non-trivial, but finite. In this paper, we prove that every abelian group with an infinite torsion subgroup admits a (Hausdorff) almost maximally almost-periodic group topology. Some open problems are also formulated.
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Let G be an abelian group. We prove that a group G admits a Hausdorff group topology τ such that the von Neumann radical n(G, τ) of (G, τ) is non-trivial and finite iff G has a non-trivial finite subgroup. If G is a topological group, then n(n(G)) 6= n(G) if and only if n(G) is not dually embedded. In particular, n(n(Z, τ)) = n(Z, τ) for any Hausdorff group topology τ on Z. We shall write our a...
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1. In view of the recent work on topological groups it is natural to consider the situation which arises when such groups act as transformation groups on various types of spaces. Such a study is begun here from the point of view of almost periodic transformation groups, the definition of which is suggested by von Neumann's paper on almost periodic functions in a group.f Compact topological tran...
متن کامل2 7 N ov 2 00 5 Almost maximally almost - periodic group topologies determined by T - sequences ∗
A sequence {an} in a group G is a T -sequence if there is a Hausdorff group topology τ on G such that an τ −→ 0. In this paper, we provide several sufficient conditions for a sequence in an abelian group to be a T -sequence, and investigate special sequences in the Prüfer groups Z(p∞). We show that for p 6= 2, there is a Hausdorff group topology τ on Z(p∞) that is determined by a T -sequence, w...
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ژورنال
عنوان ژورنال: Topology and its Applications
سال: 2009
ISSN: 0166-8641
DOI: 10.1016/j.topol.2009.04.005