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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.

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
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