On minimal non-σ-supersoluble groups

Let 𝜎={𝜎𝑖⁢⏧⁢𝑖∈𝐼} be some partition of the set ℙ of all primes. A group G is said to be 𝜎-supersoluble if all its chief factors below the 𝜎-nilpotent residual 𝐺𝔑𝜎 are cyclic. In this paper, we give a classification on minimal non-𝜎-supersoluble groups.