The one-dimensional compact connected abelian groups, called solenoids, are classified and constructed as topological subgroups of the torus Tℵ0. For an arbitrary solenoid 6 ̸= T, we exhibit a nonsplitting extension of 6 by a profinite group, dual to a nonsplitting extension 0 → tor(A) → A → F → 0 of abelian groups where F is a rank-1 torsion-free group ̸= Z. The constructed groups A are generalizations of examples of Fuchs.
ONE-DIMENSIONAL COMPACT CONNECTED ABELIAN GROUPS AND NONSPLITTING EXTENSIONS
Dikranjan D.;
2025-01-01
Abstract
The one-dimensional compact connected abelian groups, called solenoids, are classified and constructed as topological subgroups of the torus Tℵ0. For an arbitrary solenoid 6 ̸= T, we exhibit a nonsplitting extension of 6 by a profinite group, dual to a nonsplitting extension 0 → tor(A) → A → F → 0 of abelian groups where F is a rank-1 torsion-free group ̸= Z. The constructed groups A are generalizations of examples of Fuchs.File in questo prodotto:
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