Submission date: 30 September 2015.

Abstract:

The notion of almost centralizer and almost commutator are introduced and basic properties are established. They are used to study \widetilde M_c-groups, i.e., groups for which every descending chain of centralizers each having infinite index in its predecessor stabilizes after finitely many steps. The Fitting subgroup of such groups is shown to be nilpotent and a theorem of Hall for nilpotent groups is generalized to ind-definable almost nilpotent subgroups of \widetilde M_c-groups.

Mathematics Subject Classification:

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Full text arXiv 1509.09087: pdf, ps.