Formations of Finite Groups in Polynomial Time: the $\mathfrak{F}$-Radical

Abstract: For a Baer-local (composition) Fitting formation $\mathfrak{F}$ the polynomial time algorithm for the computation of the $\mathfrak{F}$-radical of a permutation group is suggested. In particular it is showed how one can compute the $\mathfrak{F}$-radical in case when $\mathfrak{F}$ is a primitive saturated formation of soluble groups. Moreover, the polynomial time algorithms for the computation of different lengthes associated with a group are presented.