On sublattices of the lattice of partially totally saturated formations of finite groups

All groups under consideration are finite. The paper studies some properties of the lattice of all $\tau-$closed totally $\omega-$saturated formations. Using methods of V.G. Safonov and L.A. Shemetkov, we prove that for any subgroup functor $\tau$ , the lattice of $\tau-$closed totally $\omega-$saturated formations is a complete sublattice of the lattice of all totally $\omega-$saturated formations. In particular, we show that the lattice of all $\tau-$closed totally saturated formations is a complete sublattice of the lattice of all totally saturated formations. Similarly, the lattice of all $\tau-$closed totally $p-$saturatedformations is a complete sublattice of the lattice of all totally $p-$saturated formations.