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On Formations of Finite Groups with the Wielandt Property for Residuals

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dc.contributor.authorBallester-Bolinches, Adolfo
dc.contributor.authorCossey, Peter (John)
dc.contributor.authorEzquerro, L
dc.date.accessioned2015-12-13T23:41:08Z
dc.date.issued2001
dc.date.updated2015-12-12T09:31:25Z
dc.description.abstractGiven two subgroups U, V of a finite group which are subnormal subgroups of their join <U, V> and a formation F, in general it is not true that (U, V)F = <UF , VF>. A formation is said to have the Wielandt property if this equality holds universally. A formation with the Wielandt property must be a Fitting class. Wielandt proved that the most usual Fitting formations (e.g., nilpotent groups and π-groups) have the Wielandt property. At present, neither a general satisfactory result on the universal validity of the Wielandt property nor a counterexample is known. In this paper a criterion for a Fitting formation to have the Wielandt property is given. As an application, it is proved that many of the known Fitting formations have the Wielandt property.
dc.identifier.issn0021-8693
dc.identifier.urihttp://hdl.handle.net/1885/94761
dc.publisherElsevier
dc.sourceJournal of Algebra
dc.subjectKeywords: Formations; Lattice properties; Residuals; Subnormal subgroups
dc.titleOn Formations of Finite Groups with the Wielandt Property for Residuals
dc.typeJournal article
local.bibliographicCitation.lastpage737
local.bibliographicCitation.startpage717
local.contributor.affiliationBallester-Bolinches, Adolfo, Universitat de Valencia
local.contributor.affiliationCossey, Peter (John), College of Physical and Mathematical Sciences, ANU
local.contributor.affiliationEzquerro, L, Universidad Publica de Navarra
local.contributor.authoruidCossey, Peter (John), u6800662
local.description.embargo2037-12-31
local.description.notesImported from ARIES
local.description.refereedYes
local.identifier.absfor010105 - Group Theory and Generalisations
local.identifier.ariespublicationMigratedxPub24434
local.identifier.citationvolume243
local.identifier.doi10.1006/jabr.2001.8823
local.identifier.scopusID2-s2.0-0035885659
local.type.statusPublished Version

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