On formations of finite groups with the Wielandt property for residuals

A. Ballester-Bolinches*, J. Cossey, L. M. Ezquerro

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    2 Citations (Scopus)

    Abstract

    Given 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.

    Original languageEnglish
    Pages (from-to)717-737
    Number of pages21
    JournalJournal of Algebra
    Volume243
    Issue number2
    DOIs
    Publication statusPublished - 15 Sept 2001

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