Almost maximally almost-periodic group topologies determined by T-sequences |
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Authors: | Gábor Lukács |
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Institution: | Department of Mathematics and Statistics, Dalhousie University, Halifax, B3H 3J5, Nova Scotia, Canada |
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Abstract: | A sequence {an} in a group G is a T-sequence if there is a Hausdorff group topology τ on G such that . 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≠2, there is a Hausdorff group topology τ on Z(p∞) that is determined by a T-sequence, which is close to being maximally almost-periodic—in other words, the von Neumann radical n(Z(p∞),τ) is a non-trivial finite subgroup. In particular, n(n(Z(p∞),τ))?n(Z(p∞),τ). We also prove that the direct sum of any infinite family of finite abelian groups admits a group topology determined by a T-sequence with non-trivial finite von Neumann radical. |
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Keywords: | 22A05 54A20 22C05 20K45 54H11 |
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