Abstract We introduce a simple equivalence relation on strongly minimal sets in a structure of finite Morley rank, which corresponds, in stability theory, to the non-orthogonality of the associated types. We use it in a group 𝐺 of finite Morley rank to define, for each strongly minimal set 𝑋, two connected normal subgroups M G (X) M₆ (X) and W G (X) W₆ (X). When 𝐺 is connected, these subgroups provide a central decomposition of 𝐺 that yields a direct product decomposition of G / Z (G) G/Z (G) into unidimensional factors, as well as a central decomposition of its derived subgroup into unidimensional subgroups.
Bentbib et al. (Wed,) studied this question.