On $\omega$-Schunck classes and generalized projectors of finite groups

Let $\omega$ be a non-empty set of primes. The operations $\mathrm{Q}_{\omega}$, $\mathrm{P}_{\omega}$ and $\mathrm{E}_{\Phi\omega}$ on classes of finite groups are introduced and studied. The $\omega$-Schunck class is defined and its applications to finding generalized projectors of groups and studying their properties are obtained.