Equationally separable classes of groups
Group Theory
2025-03-04 v2
Abstract
Over each nontrivial finite group , there exists a finite system of equations having no solutions in larger finite groups but having a solution in a periodic group containing . 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.
Cite
@article{arxiv.2502.05831,
title = {Equationally separable classes of groups},
author = {Alexander Buturlakin and Anton Klyachko and Denis Osin},
journal= {arXiv preprint arXiv:2502.05831},
year = {2025}
}
Comments
An inaccuracy in the proof of Theorem 5.1 (6) has been fixed