  For a wide family of formations $\mathfrak{F}$ it is proved that the $
\mathfrak{F}$-residual of a permutation finite group can be computed in a
polynomial time. Moreover, if in the previous case $\mathfrak{F}$ is
hereditary, then an $\mathfrak{F}$-subnormality of a subgroup can be checked in
a polynomial time.
