Injectors with a central socle in a finite solvable group

In response to an Open Question of Doerk and Hawkes (1992) [2, IX §4, p. 628], we shall describe three constructions for the Zπ-injectors of a finite solvable group, where Zπ is the Fitting class formed by the finite solvable groups whose π-socle is central (and π is a set of prime numbers).