Divisible Rigid Groups. Morley Rank

Let G be a countable saturated model of the theory 𝔗m of divisible m-rigid groups. Fix the splitting G1G2 . . .Gm of a group G into a semidirect product of Abelian groups. With each tuple (n1, . . . , nm) of nonnegative integers we associate an ordinal α = ωm−1nm+ . . . + ωn2 + n1 and denote by G(α) the set G1n1×G2n2×…×Gmnm\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {G}_1^{n_1}\times {G}_2^{n_2}\times \dots \times {G}_m^{n_m} $$\end{document}, which is definable over G in Gn1+…+nm\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {G}^{n_1+\dots +{n}_m} $$\end{document}. Then the Morley rank of G(α) with respect to G is equal to α. This implies that RM (G) = ωm−1 + ωm−2 + . . . + 1.