2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/142923One of the central tools in the classification of simple algebraic groups is the distinction between semisimple subgroups and unipotent subgroups. It is not a priori clear how to make this distinction for torsion-free subgroups of a group of finite Morley rank. We exploit the ``graded'' notion of 0-unipotence to develop a Sylow theory for torsion-free subgroups of a solvable group of finite Morley rank. This Sylow theory provides a robust alternative to the usual theory of Carter subgroups, and will be used in the analysis of intersections of Borel subgroups in minimal simple groups.LogicGroup Theory03C60, 20G99text