Факторизация локально нормальных классов фиттинга

It is proved that if F or G are π -normal Fitting classes, then FG is normal in π S . The following result was obtained: if F and G are Fitting classes, such that π F ⊆ S and π G ⊆ S , then the following statements hold: a Fitting class FG is normal in π S if and only if FG∗ is π -normal; a Fitting class F∗G is normal in π S if and only if π F∗G∗ = S ; if exists a set σ ⊆π of primes such that F∗S = F∗ σ and σ π S G∗ = S , then π F∗G∗ = S ; if either F or G is normal in π S , then FG is π S -norma