turkmath.org

Every finite group G has a normal series each of whose factors either is soluble or is a direct product of nonabelian simple groups. In recent joint work with E. Khukhro we defined the nonsoluble length λ(G) as the number of nonsoluble factors in a shortest series of this kind. Upper bounds for λ(G) appear in the study of various problems on finite, residually finite, and profinite groups. In particular, such bounds played important role in the Hall-Higman reduction theorem for the restricted Burnside problem. In the talk several new results on λ(G) will be discussed.