Hartley Sets and Injectors of a Finite Group

Abstract

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 π-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.