Formations of Finite Groups in Polynomial Time: the F-Radical

Abstract

For a Baer-local (composition) Fitting formation F the polynomial time algorithm for the computation of the F-radical of a permutation group is suggested. In particular it is showed how one can compute the F-radical in case when 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.