On $p$-nonsingular systems of equations over solvable groups
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866913565025239040 |
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| author | Mikheenko, Mikhail A. |
| author_facet | Mikheenko, Mikhail A. |
| contents | Any group that has a subnormal series, in which all factors are abelian and all except the last one are $p'$-torsion-free, can be embedded into a group with a subnormal series of the same length, with the same properties and such that any $p$-nonsingular system of equations over this group is solvable in this group itself. This helps us to prove that the minimal order of a metabelian group, over which there is a unimodular equation that is unsolvable in metabelian groups, is 42. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2309_09096 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On $p$-nonsingular systems of equations over solvable groups Mikheenko, Mikhail A. Group Theory 20F70 (Primary), 16S34, 16S50 (Secondary) Any group that has a subnormal series, in which all factors are abelian and all except the last one are $p'$-torsion-free, can be embedded into a group with a subnormal series of the same length, with the same properties and such that any $p$-nonsingular system of equations over this group is solvable in this group itself. This helps us to prove that the minimal order of a metabelian group, over which there is a unimodular equation that is unsolvable in metabelian groups, is 42. |
| title | On $p$-nonsingular systems of equations over solvable groups |
| topic | Group Theory 20F70 (Primary), 16S34, 16S50 (Secondary) |
| url | https://arxiv.org/abs/2309.09096 |