Equationally separable classes of groups

Alexander Buturlakin; Anton Klyachko; Denis Osin

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arXiv · 2502.05831

Equationally separable classes of groups

Alexander Buturlakin·Anton Klyachko·Denis Osin

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Abstract

Over each nontrivial finite group $G$, there exists a finite system of equations having no solutions in larger finite groups but having a solution in a periodic group containing $G$. We prove several similar facts about amenable, orderable, locally indicable, solvable, nilpotent, and other classes of groups. As a byproduct, we also show that any amalgam of two countable periodic groups with finite intersection embeds into a periodic group, thereby answering a 1960 question of B. Neumann in the countable case.

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Alexander Buturlakin, Anton Klyachko, Denis Osin. 2025-02-09. Equationally separable classes of groups. https://arxiv.org/abs/2502.05831

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