Finite groups with given systems of generalised σ-permutable subgroups

Let σ = {σi|i ∈ I } be a partition of the set all primes ℙ and G finite group. A ℋ subgroups is said to complete Hall σ-set if every member ≠1 σi-subgroup for some i contains exactly one such that σi ⌒ π(G) ≠ ∅. group σ-primary it σi-group i. subgroup be: σ-permutable in possesses AH x H xA G; σ-subnormal there chain A0 ≤ A1 … At either Ai − 1 ⊴ or /(Ai 1)Ai 1, …, t;