A note on finite groups generated by their subnormal subgroups

Abstract

Following the theory of operators created by Wielandt, we ask for what kind of formations ℱ and for what kind of subnormal subgroups U and y of a finite group G we have that the ℱ-residual of the subgroup generated by two subnormal subgroups of a group is the subgroup generated by the ℱ-residuals of the subgroups. In this paper we provide an answer whenever U is quasinilpotent and ℱ is either a Fitting formation or a saturated formation closed for quasinilpotent subnormal subgroups. © Edinburgh Mathematical Society 2001.