Formations of Finite Groups in Polynomial Time: the $\mathfrak{F}$-Hypercenter
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916329597960192 |
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| author | Murashka, Viachaslau I. |
| author_facet | Murashka, Viachaslau I. |
| contents | For a wide family of formations $\mathfrak{F}$ (which includes Baer-local formations) it is proved that the $ \mathfrak{F}$-hypercenter of a permutation finite group can be computed in polynomial time. 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, $p$-nilpotent, supersoluble, $w$-supersoluble and $SC$-groups. For some of these formations algorithms for the computation of the intersection of all maximal $\mathfrak{F}$-subgroups are suggested. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_13606 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Formations of Finite Groups in Polynomial Time: the $\mathfrak{F}$-Hypercenter Murashka, Viachaslau I. Group Theory 20D10, 20B40 For a wide family of formations $\mathfrak{F}$ (which includes Baer-local formations) it is proved that the $ \mathfrak{F}$-hypercenter of a permutation finite group can be computed in polynomial time. 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, $p$-nilpotent, supersoluble, $w$-supersoluble and $SC$-groups. For some of these formations algorithms for the computation of the intersection of all maximal $\mathfrak{F}$-subgroups are suggested. |
| title | Formations of Finite Groups in Polynomial Time: the $\mathfrak{F}$-Hypercenter |
| topic | Group Theory 20D10, 20B40 |
| url | https://arxiv.org/abs/2407.13606 |