Equationally separable classes of groups

2025/02/09 by A. Buturlakin, Buturlakin, Alexander, A. Klyachko +3
Mathematics · #FOS: Mathematics #Group Theory (math.GR) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2502.05831

openalex publication_date 2025/02/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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