On Formations of Finite Groups with the Wielandt Property for Residuals (original) (raw)

dedicated to k. doerk on his 60th birthday Given two subgroups U V of a finite group which are subnormal subgroups of their join U V and a formation , in general it is not true that U V = U V. 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