Some structure theorems for \(\omega\)-stable groups (Q1102271)

The author proves here that every locally supersolvable group of finite Morley rank is nilpotent-by-finite, and hence hypercyclic. This is motivated by the analogous result of \textit{C. A. Higgins} [J. Lond. Math. Soc., II. Ser. 20, 53-59 (1979; Zbl 0413.20028)] about CZ-groups: both CZ-groups and groups of finite Morley rank are abstractions of algebraic groups and so are reasonably expected to share the same structure theorems, and in fact it is an open question whether groups of finite Morley rank are CZ-groups, i.e. carry a \(T_ 1\) topology with the DCC on closed sets, and such that the following maps: \(x\to ax\), xa, \(x^{-1}\), \(xax^{-1}\), are continuous.