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JOURNALS // Trudy Instituta Matematiki i Mekhaniki UrO RAN // Archive

Trudy Inst. Mat. i Mekh. UrO RAN, 2025 Volume 31, Number 1, Pages 154–165 (Mi timm2159)

Formations of finite groups in polynomial time ii: the $\mathfrak{F}$-hypercenter and its generalizations

V. I. Murashka

Gomel State University named after Francisk Skorina

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

Keywords: finite group, $\mathfrak{F}$-hypercenter, Baer-local formation, permutation group computation, polynomial time algorithm.

UDC: 512.542, 519.6

MSC: 20D10, 20B40

Received: 11.10.2024
Revised: 08.01.2025
Accepted: 13.01.2025

Language: English

DOI: 10.21538/0134-4889-2025-31-1-154-165



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© Steklov Math. Inst. of RAS, 2025