Submission date: 4 May 2012.

Abstract:

Let G be an arbitrary group. We show that if the Fitting subgroup of G is nilpotent then it is definable. We show also that the class of groups whose Fitting subgroup is nilpotent of class at most n is elementary. We give an example of a group (arbitrary saturated) whose Fitting subgroup is definable but not nilpotent. Similar results for the soluble radical are given.

Mathematics Subject Classification:

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Full text arXiv 1205.0573: pdf, ps.