One-dimensional Compact Connected Abelian Groups and Nonsplitting Extensions
Document Type
Peer-Reviewed Article
Publication Date
2025
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 Σ≠T, we exhibit a nonsplitting extension of Σ 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.
DOI
10.1216/jca.2025.17.301
Recommended Citation
Dikranjan, D., Lewis, W., Loth, P., & Mader, A. (2025). One-dimensional compact connected abelian groups and nonsplitting extensions. Journal of Commutative Algebra, 17(3), 301-322. Doi: 10.1216/jca.2025.17.301
