О полугруппе пи-нормальных классов Фиттинга

Abstract

Установлено, что произведение двух классов Фиттинга конечных пи-групп является пи-нормальным классом Фиттинга при условии, что пи-нормален второй сомножитель = In this paper for every non empty -multitude of primes the concept of -normal Fitting class as a Fitting class, normal in E class of all finite -groups is introduced. The issue of  normality of Fitting classes of finite -groups product is studied. It is established that the product of two Fitting classes of finite -groups is a -normal Fitting class, if the second multiplier is a -normal Fitting class. This property signifies that the algebra P,  is a semigroup, where P is the set of all -normal Fitting classes and « » is the multiplication operation of Fitting classes. The main theorem of this paper extends the known Laue’s result on the conditions for products of Fitting classes of finite groups to be normal in the class E of all finite groups.