We explore a non-abelian torsion theory in the category of preordered groups: the objects of its torsion-free subcategory are the partially ordered groups, whereas the objects of the torsion subcategory are groups (with the total order). The reflector from the category of preordered groups to this torsion-free subcategory has stable units, and we prove that it induces a monotone-light factorization system. We describe the coverings relative to the Galois structure naturally associated with this reflector, and explain how these coverings can be classified as internal actions of a Galois groupoid. Finally, we prove that in the category of preordered groups there is also a pretorsion theory, whose torsion subcategory can be identified with a category of internal groups. This latter is precisely the subcategory of protomodular objects in the category of preordered groups, as recently discovered by Clementino, Martins-Ferreira, and Montoli.

我们在预排序组的类别中探索一种非阿贝尔扭转理论：无扭转子类别的对象是部分有序的组，而扭转子类别的对象是组（具有总的顺序）。从预排序组的类别到此无扭转子类别的反射器具有稳定的单位，并且我们证明了它诱发了单调光分解系统。我们描述与该反射器自然相关的Galois结构相关的覆盖物，并解释如何将这些覆盖物归类为Galois类群的内部作用。最后，我们证明了在预排序组的类别中还存在一种扭转理论，其扭转子类别可以通过内部组的类别进行识别。