6533b86ffe1ef96bd12cd278

RESEARCH PRODUCT

A note on finite groups generated by their subnormal subgroups

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AbstractFollowing the theory of operators created by Wielandt, we ask for what kind of formations $\mathfrak{F}$ and for what kind of subnormal subgroups $U$ and $V$ of a finite group $G$ we have that the $\mathfrak{F}$-residual of the subgroup generated by two subnormal subgroups of a group is the subgroup generated by the $\mathfrak{F}$-residuals of the subgroups.In this paper we provide an answer whenever $U$ is quasinilpotent and $\mathfrak{F}$ is either a Fitting formation or a saturated formation closed for quasinilpotent subnormal subgroups.AMS 2000 Mathematics subject classification: Primary 20F17; 20D35