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arXiv · 2306.05214

Generic isomorphism classes of abelian groups

Udayan B. Darji·Márton Elekes·Tamás Kátay·Anett Kocsis·Máté Pálfy
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Abstract

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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BibTeXRIS

Udayan B. Darji, Márton Elekes, Tamás Kátay, Anett Kocsis, Máté Pálfy. 2023-06-08. Generic isomorphism classes of abelian groups. https://arxiv.org/abs/2306.05214

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