Geodesic
$p$-Nonsingular systems of equations over solvable groups
Sbornik. Mathematics, Tome 215 (2024) no. 6, pp. 775-789 Cet article a éte moissonné depuis la source Math-Net.Ru

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Any group that has a subnormal series all factors in which are abelian and all factors 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. Using this we prove that the minimal order of a metabelian group over which there exists a unimodular equation that is unsolvable in metabelian groups is $42$. Bibliography: 14 titles.
Keywords: equations over groups, group rings, solvable groups. 
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M. A. Mikheenko. $p$-Nonsingular systems of equations over solvable groups. Sbornik. Mathematics, Tome 215 (2024) no. 6, pp. 775-789. http://geodesic.mathdoc.fr/item/SM_2024_215_6_a3/

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