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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2602.00631 |
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| _version_ | 1866911413058928640 |
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| author | Dubickas, Artūras Smyth, Chris |
| author_facet | Dubickas, Artūras Smyth, Chris |
| contents | In this article, we first describe all nonempty sets of integers S with the property that for all n and m in S, not necessarily distinct, the set {n-m,n+m} intersected with S consists of a single element. These are the sets with at most two elements, one of which is 0, and the infinite sets {rk}, where r is a fixed positive integer and k runs over all integers not divisible by 3.
In the later sections, we solve the analogous problem for subsets of abelian groups. We also discuss, but do not completely solve, the analogous problem for nonabelian groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_00631 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Subsets of abelian groups closed under addition or subtraction Dubickas, Artūras Smyth, Chris Group Theory 05B10, 11B13, 20M14, 20M75 In this article, we first describe all nonempty sets of integers S with the property that for all n and m in S, not necessarily distinct, the set {n-m,n+m} intersected with S consists of a single element. These are the sets with at most two elements, one of which is 0, and the infinite sets {rk}, where r is a fixed positive integer and k runs over all integers not divisible by 3. In the later sections, we solve the analogous problem for subsets of abelian groups. We also discuss, but do not completely solve, the analogous problem for nonabelian groups. |
| title | Subsets of abelian groups closed under addition or subtraction |
| topic | Group Theory 05B10, 11B13, 20M14, 20M75 |
| url | https://arxiv.org/abs/2602.00631 |