On $p$-compact group topologies on direct sums of ${\mathbb Q}

We prove that if $p$ is a selective ultrafilter then ${\mathbb Q}^{(\kappa)}$ has a $p$-compact group topology without non-trivial convergent sequences, for each infinite cardinal $\kappa =\kappa^\omega$. In particular, this gives the first arbitrarily large examples of countably compact groups with...

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Bibliographic Details
Main Authors Bellini, Matheus Koveroff, Rodrigues, Vinicius de Oliveira, Tomita, Artur Hideyuki
Format Journal Article
LanguageEnglish
Published 11.04.2019
Subjects
Mathematics - General Topology
Mathematics - Group Theory
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Summary:We prove that if $p$ is a selective ultrafilter then ${\mathbb Q}^{(\kappa)}$ has a $p$-compact group topology without non-trivial convergent sequences, for each infinite cardinal $\kappa =\kappa^\omega$. In particular, this gives the first arbitrarily large examples of countably compact groups without non-trivial convergent sequences that are torsion-free.
DOI:10.48550/arxiv.1904.05928