Finite groups with Hall $\pi$-subgroups

New classes of finite groups with Hall $\pi$-subgroups that have the Sylow properties are constructed and studied. The classes of groups $C_\pi$ and $D_\pi$ introduced by P. Hall are substantially extended. Necessary and sufficient conditions are established under which a finite group has Hall $\pi$-subgroups. $D$-Theorems generalizing $D$-theorems of P. Hall, Wielandt, Baer, and Hartley are obtained.
Bibliography: 30 titles.