Formations of Finite Groups in Polynomial Time: the \mathfrakF-Hypercenter

2024/07/18 by Viachaslau I. Murashka, Murashka, Viachaslau I.
Computer Science · Mathematics · #20B40 #20D10 #FOS: Mathematics #Group Theory (math.GR) #Matrix Theory and Algorithms #Polynomial and algebraic computation #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2407.13606

openalex publication_date 2024/07/18 · openalex created_date 2024/09/09 · openalex updated_date 2026/07/28

Abstract

For a wide family of formations \mathfrakF (which includes Baer-local formations) it is proved that the \mathfrakF-hypercenter of a permutation finite group can be computed in polynomial time. In particular, the algorithms for computing the \mathfrakF-hypercenter for the following classes of groups are suggested: hereditary local formations with the Shemetkov property, rank formations, formations of all quasinilpotent, Sylow tower, p-nilpotent, supersoluble, w-supersoluble and SC-groups. For some of these formations algorithms for the computation of the intersection of all maximal \mathfrakF-subgroups are suggested.

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