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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Bibliographic Details
Published in:arXiv.org 2023-06
Main Authors: Darji, Udayan B, Elekes, Márton, Kátay, Tamás, Kocsis, Anett, Máté Pálfy
Format: Article
Language:English
Subjects:
Group theory
Isomorphism
Solenoids
Online Access:Get full text
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Summary: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.
ISSN:2331-8422