Torsion theories and coverings of preordered groups (Q1996102)

This article is a contribution to the abstract categorical study of preordered groups. It proves especially that the pair of full subcategories of \textit{groups} (endowed with the trivial preorder: \(g\le h\) for all \(g, h\)) and of \textit{partially ordered groups} form a \textit{torsion theory}, in the non-abelian sense [\textit{M. Clementino} et al., J. Algebra 305, No. 1, 98--129 (2006; Zbl 1121.18010)]. It studies also categorical Galois theoretic aspects of preordered groups.