Formations of finite groups in polynomial time: the $\mathfrak{F}$-radical and the $\mathfrak{F}$-length

For a Baer-local (composition) Fitting formation $\mathfrak{F}$ of finite groups the algorithm for the computation of the $\mathfrak{F}$-radical of a permutation finite group which runs in polynomial time from its degree is herein suggested. It is shown how one can compute the $\mathfrak{F}$-radical in case when $\mathfrak{F}$ is a primitive saturated formation of soluble finite groups. The algorithms for the computation of different lengths associated with a finite group (the generalised Fitting height, the non-$p$-soluble length and etc.) are presented. In the case of a permutation group these algorithms run in polynomial time from its degree.