Formations of finite groups in polynomial time: the F-radical and the F-length - Murashka, Viachaslau I. (Journal of the Belarusian State University. Mathematics and Informatics, 2025)
For a Baer-local (composition) Fitting formation F of finite groups the algorithm for the computation of the 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 F-radical in case when 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.
Keywords: finite group; permutation group computation; Baer-local formation; Fitting formation; F-radical; F-length; polynomial time algorithm