Solvable and nilpotent structures (Q1823235)

Summary: In Arch. Math. Logic 27, No.2, 193-197 (1988; Zbl 0661.03026), we have proven that every \(non\)-\(\aleph_ 1\)-categorical connected nilpotent group of finite Morley rank has the center Z(G) with RM(Z(G))\(\geq 2\). If a connected nilpotent group has finite Morley rank, then it is easy to see that the center is infinite. So the above result shows if G is \(non\)- \(\aleph_ 1\)-categorical the center has a rather complicated structure. The present paper is a natural continuation of the mentioned paper. Here we introduce the notion of *-nilpotency, and prove *-versions of our earlier results (see Theorems 2.3, and 2.6). Since our setting is rather general, we can apply our results to \(\omega\)-stable ring theory.