Resumen de Fischer classes in finite groups

José Ramón Martínez Verduch

• In [2] we define the concept of a "pi-satured Fitting class". The present work investigates a particular type of such classes, those we have called "Fischer classes relative to pi", which allow us to present a version of Fischer's theorem valid for pi-solvable groups. We have followed the type of proof of the cited Hartley Theorem, which is essentially based on the behaviour of the injectors of a group G with respect to the complements of self-centralizing factors of G, with the necessary modifications not disposing of the hypothesis of solubility.