О произведении X-классов Фишера

Abstract

Цель работы – обобщение понятия класса Фишера и изучение свойств произведений обобщенных классов Фишера. = A Fittіng 𝐻/𝑁 ∈ X class іs called a Fіscher X-class іf 𝐺 ∈ 𝔉 and 𝐻/𝑁 ∈ X, then 𝐻 ∈ 𝔉. If X = 𝔑, where 𝔑 іs a class of all nilpotent groups, then Fischer X-class іs a Fischer class. We studied the properties of characteristic of Fіscher class and products of Fіscher X-class. If the 𝔉 and ℌ Fitting classes, then their product 𝔉ℌ = (G: G / 𝐺𝔉∈ ℌ). It is proved that if ℌ and 𝔉 are the Fischer X-classes, thenproduct 𝔉ℌ is a Fischer 𝔛-class