Formations of Finite Groups in Polynomial Time: $\mathfrak{F}$-residuals and $\mathfrak{F}$-subnormality

Abstract: 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.