Abstract:
The finite groups that can be represented as a product of pairwise permutable subgroups with formational restrictions on factors
and their partial products are studied. In particular, the description of solvable hereditary saturated formations of groups with
the property $\mathcal{P}_2$ introduced by B. Amberg, A.S. Kazarin and Hefling is obtained.
Keywords:finite group, product of pairwise permutable subgroups, formation with the $\mathcal{P}_2$ property, formation with the Kegel property, formation with the Shemetkov property.