The Fitting subgroup of a stable group. (English) Zbl 0831.03018
The author proves the following results: The Fitting subgroup of a stable group is definable. The generalised Fitting subgroup (i.e. the central product of the Fitting subgroup and the layer) of such a group is type- definable. The radical (i.e. the maximal soluble normal subgroup) of a superstable group exists and is definable; it is also the maximal locally soluble normal subgroup.
Reviewer: S.R.Kogalovskij (Ivanovo)
MSC:
03C60 | Model-theoretic algebra |
03C45 | Classification theory, stability, and related concepts in model theory |
20A15 | Applications of logic to group theory |
20F19 | Generalizations of solvable and nilpotent groups |
20E07 | Subgroup theorems; subgroup growth |