On $p$-nonsingular systems of equations over solvable groups
Abstract
Any group that has a subnormal series, in which all factors are abelian and all except the last one are -torsion-free, can be embedded into a group with a subnormal series of the same length, with the same properties and such that any -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.
Cite
@article{arxiv.2309.09096,
title = {On $p$-nonsingular systems of equations over solvable groups},
author = {Mikhail A. Mikheenko},
journal= {arXiv preprint arXiv:2309.09096},
year = {2024}
}
Comments
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