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A remark on the definability of the Fitting subgroup and the soluble radical

Authors
  • Houcine, A. Ould
Type
Preprint
Publication Date
May 02, 2012
Submission Date
May 02, 2012
Identifiers
arXiv ID: 1205.0573
Source
arXiv
License
Yellow
External links

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.

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