Certain residual properties of HNN-extensions with normal associated subgroups
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866913815940038656 |
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| author | Sokolov, E. V. Tumanova, E. A. |
| author_facet | Sokolov, E. V. Tumanova, E. A. |
| contents | Let $\mathbb{E}$ be the HNN-extension of a group $B$ with subgroups $H$ and $K$ associated according to an isomorphism $φ\colon H \to K$. Suppose that $H$ and $K$ are normal in $B$ and $(H \cap K)φ= H \cap K$. Under these assumptions, we prove necessary and sufficient conditions for $\mathbb{E}$ to be residually a $\mathcal{C}$-group, where $\mathcal{C}$ is a class of groups closed under taking subgroups, quotient groups, and unrestricted wreath products. Among other things, these conditions give new facts on the residual finiteness and the residual $p$-finiteness of the group $\mathbb{E}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_00262 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Certain residual properties of HNN-extensions with normal associated subgroups Sokolov, E. V. Tumanova, E. A. Group Theory 20E26 (Primary) 20E06 (Secondary) Let $\mathbb{E}$ be the HNN-extension of a group $B$ with subgroups $H$ and $K$ associated according to an isomorphism $φ\colon H \to K$. Suppose that $H$ and $K$ are normal in $B$ and $(H \cap K)φ= H \cap K$. Under these assumptions, we prove necessary and sufficient conditions for $\mathbb{E}$ to be residually a $\mathcal{C}$-group, where $\mathcal{C}$ is a class of groups closed under taking subgroups, quotient groups, and unrestricted wreath products. Among other things, these conditions give new facts on the residual finiteness and the residual $p$-finiteness of the group $\mathbb{E}$. |
| title | Certain residual properties of HNN-extensions with normal associated subgroups |
| topic | Group Theory 20E26 (Primary) 20E06 (Secondary) |
| url | https://arxiv.org/abs/2505.00262 |