Generic isomorphism classes of abelian groups

Generic isomorphism classes of abelian groups

We prove that the universal solenoid is the generic (in the sense of Baire category) connected compact metrizable abelian group. We also settle the dual problem in the sense of Pontryagin duality: \((\mathbb{Q},+)\), which is the dual of the universal solenoid, is the generic countably infinite tors...

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Veröffentlicht in:arXiv.org 2023-06
Hauptverfasser: Darji, Udayan B, Elekes, Márton, Kátay, Tamás, Kocsis, Anett, Máté Pálfy
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Group theory
Isomorphism
Solenoids
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Máté Pálfy
description We prove that the universal solenoid is the generic (in the sense of Baire category) connected compact metrizable abelian group. We also settle the dual problem in the sense of Pontryagin duality: \((\mathbb{Q},+)\), which is the dual of the universal solenoid, is the generic countably infinite torsion-free abelian group.
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subjects Group theory
Isomorphism
Solenoids
title Generic isomorphism classes of abelian groups
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