A generalization of a Hall theorem

Let sigma = {sigma(i) vertical bar i is an element of I} be some partition of the set P of all primes, that is, P = boolean OR(i is an element of I)sigma(i) and sigma(i) boolean AND sigma(j) = circle divide for all i not equal j. We say that a finite group G is sigma-soluble if every chief factor H/K of G is a sigma(i)-group for some i = i(H/K) is an element of I. We give some characterizations of finite sigma-soluble groups.