Hartley Sets and Injectors of a Finite Group

By a Fitting set of a group $G$ one means a nonempty set of subgroups $\mathscr F$ of a finite group $G$ which is closed under taking normal subgroups, their products, and conjugations of subgroups. In the present paper, the existence and conjugacy of $\mathscr F$-injectors of a partially $\pi$-solvable group $G$ is proved and the structure of $\mathscr F$-injectors is described for the case in which $\mathscr F$ is a Hartley set of $G$.