On $p$-nonsingular systems of equations over solvable groups
| Autor: | Mikheenko, Mikhail A. |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.4213/sm10009e |
| Popis: | 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. Comment: 12 pages, 1 table. v3: the beginning of introduction rewritten; inaccuracies in Section 2 corrected (as well as some other minor inaccuracies) - the results remain the same; a shorter proof for Section 3 presented, thanks to an anonymous referee; Table 1 addeed; a new reference added |
| Databáze: | arXiv |
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