Explicit construction of benign subgroup for Higman's reversing operation
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866918073238290432 |
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| author | Mikaelian, V. H. |
| author_facet | Mikaelian, V. H. |
| contents | For the Higman reversing operation $ρ$ and for a set of integer-valued functions $\mathcal X$ the following has been proved. Let the subgroup $A_{\mathcal X}$ be benign in the free group $F$, let the respective finitely presented overgroup $K_{\mathcal X}$ with its finitely generated subgroup $L_{\mathcal X}$ be given for $A_{\mathcal X}$ explicitly, and let the set $\mathcal Y = ρ\mathcal X$ be obtained from $\mathcal X$ by the reversing operation $ρ$. Then $A_{\mathcal Y}$ also is benign in $F$ and, moreover, the finitely presented overgroup $K_{\mathcal Y}$ with its finitely generated subgroup $L_{\mathcal Y}$ can also be given explicitly for it. The current work is a step in development of a general algorithm for construction of explicit Higman embeddings of recursive groups into finitely presented groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_12442 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Explicit construction of benign subgroup for Higman's reversing operation Mikaelian, V. H. Group Theory 20F05, 20E06, 20E07 For the Higman reversing operation $ρ$ and for a set of integer-valued functions $\mathcal X$ the following has been proved. Let the subgroup $A_{\mathcal X}$ be benign in the free group $F$, let the respective finitely presented overgroup $K_{\mathcal X}$ with its finitely generated subgroup $L_{\mathcal X}$ be given for $A_{\mathcal X}$ explicitly, and let the set $\mathcal Y = ρ\mathcal X$ be obtained from $\mathcal X$ by the reversing operation $ρ$. Then $A_{\mathcal Y}$ also is benign in $F$ and, moreover, the finitely presented overgroup $K_{\mathcal Y}$ with its finitely generated subgroup $L_{\mathcal Y}$ can also be given explicitly for it. The current work is a step in development of a general algorithm for construction of explicit Higman embeddings of recursive groups into finitely presented groups. |
| title | Explicit construction of benign subgroup for Higman's reversing operation |
| topic | Group Theory 20F05, 20E06, 20E07 |
| url | https://arxiv.org/abs/2506.12442 |