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arXiv · 2309.09096

On $p$-nonsingular systems of equations over solvable groups

Mikhail A. Mikheenko
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Abstract

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.

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Mikhail A. Mikheenko. 2024-01-23. On $p$-nonsingular systems of equations over solvable groups. https://doi.org/10.4213/sm10009e

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