Finite groups with given systems of K-𝔘-subnormal subgroups

Abstract

A subgroup H of a finite group G is called 𝔘-subnormal in Kegel’s sense or K-𝔘-subnormal in G if there exists a chain of subgroups H = H₀ ≤ H₁ ≤ . . . ≤ Ht = G such that either Hᵢ₋₁ is normal in Hᵢ or Hᵢ/(Hᵢ₋₁)Hᵢ is supersoluble for any i = 1, . . . , t. We describe finite groups for which every 2-maximal or every 3-maximal subgroup is K-𝔘-subnormal.