If G is a finite soluble group in which the centralizer of every non-trivial element is metabelian (or nilpotent-by-abelian), then G has derived length at most 4 (respectively, the third term of the derived series is nilpotent).
Finite soluble groups with metabelian centralizers
JABARA, Enrico
2015-01-01
Abstract
If G is a finite soluble group in which the centralizer of every non-trivial element is metabelian (or nilpotent-by-abelian), then G has derived length at most 4 (respectively, the third term of the derived series is nilpotent).
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