This interesting and substantial paper is devoted to answer an open question of K. Doerk and T. Hawkes [Finite soluble groups. De Gruyter Expositions in Mathematics 4. Berlin: W. de Gruyter (1992; Zbl 0753.20001)] concerning the description of the injectors associated to the Fitting class \(\mathcal F^\pi\) of all finite soluble groups \(G\) whose \(\pi\)-socle, that is, the subgroup generated by the minimal normal \(\pi\)-subgroups of \(G\), \(\pi\) a set of primes, is contained in the centre of \(G\). The authors describe three types of constructions for the \(\mathcal F^\pi\)-injectors with the help of many nice auxiliary results. Some interesting examples are also presented.