Journal of AlgebraVolume 422, 15 January 2015, Pages 318-333Finite soluble groups with metabelian centralizersAuthor links open overlay panelCarlo Casolo a, Enrico Jabara bShow moreShareCitehttps://doi.org/10.1016/j.jalgebra.2014.09.032Get rights and contentUnder an Elsevier user licenseopen archiveAbstractIf 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).Previous article in issueNext article in issueMSC20D1020F14KeywordsGroup theoryFinite soluble groupsCentralizersRecommended articlesCited by (0)Copyright © 2014 Elsevier Inc. All rights reserved.