  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.
