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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2502.05831 |
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| _version_ | 1866929737552625664 |
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| author | Buturlakin, Alexander Klyachko, Anton Osin, Denis |
| author_facet | Buturlakin, Alexander Klyachko, Anton Osin, Denis |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_05831 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Equationally separable classes of groups Buturlakin, Alexander Klyachko, Anton Osin, Denis Group Theory 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. |
| title | Equationally separable classes of groups |
| topic | Group Theory |
| url | https://arxiv.org/abs/2502.05831 |