Orbit-blocking words in free groups
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866913979595489280 |
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| author | Koch-Hyde, Lucy O'Connor, Siobhan Olive, Eamonn Shpilrain, Vladimir |
| author_facet | Koch-Hyde, Lucy O'Connor, Siobhan Olive, Eamonn Shpilrain, Vladimir |
| contents | By strengthening known results about primitivity-blocking words in free groups, we prove that for any nontrivial element w of a free group of finite rank, there are words that cannot be subwords of any cyclically reduced automorphic image of w. This has implications for the average-case complexity of a variant of Whitehead's problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_00477 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Orbit-blocking words in free groups Koch-Hyde, Lucy O'Connor, Siobhan Olive, Eamonn Shpilrain, Vladimir Group Theory Computational Complexity By strengthening known results about primitivity-blocking words in free groups, we prove that for any nontrivial element w of a free group of finite rank, there are words that cannot be subwords of any cyclically reduced automorphic image of w. This has implications for the average-case complexity of a variant of Whitehead's problem. |
| title | Orbit-blocking words in free groups |
| topic | Group Theory Computational Complexity |
| url | https://arxiv.org/abs/2505.00477 |