HNN extensions of free groups with equal associated subgroups of finite index: polynomial time word problem
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915810544451584 |
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| author | Shen, Hanwen Ushakov, Alexander |
| author_facet | Shen, Hanwen Ushakov, Alexander |
| contents | Let $G=F\ast_φt$ be an HNN extension of a free group $F$ with two equal associated normal subgroups $H_1 = H_2$ of finite index. We prove that the word problem in $G$ is decidable in polynomial time. This result extends to the case where the subgroups $H_1=H_2$ are not normal, provided that the isomorphism $φ:H_1\to H_2$ satisfies an additional condition described in Section 5. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_03801 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | HNN extensions of free groups with equal associated subgroups of finite index: polynomial time word problem Shen, Hanwen Ushakov, Alexander Group Theory Computational Complexity Combinatorics Let $G=F\ast_φt$ be an HNN extension of a free group $F$ with two equal associated normal subgroups $H_1 = H_2$ of finite index. We prove that the word problem in $G$ is decidable in polynomial time. This result extends to the case where the subgroups $H_1=H_2$ are not normal, provided that the isomorphism $φ:H_1\to H_2$ satisfies an additional condition described in Section 5. |
| title | HNN extensions of free groups with equal associated subgroups of finite index: polynomial time word problem |
| topic | Group Theory Computational Complexity Combinatorics |
| url | https://arxiv.org/abs/2510.03801 |