On soficity for certain fundamental groups of graphs of groups
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929468096905216 |
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| author | Gao, David Elayavalli, Srivatsav Kunnawalkam Mj, Mahan |
| author_facet | Gao, David Elayavalli, Srivatsav Kunnawalkam Mj, Mahan |
| contents | In this note we study a family of graphs of groups over arbitrary base graphs where all vertex groups are isomorphic to a fixed countable sofic group $G$, and all edge groups $H<G$ are such that the embeddings of $H$ into $G$ are identical everywhere. We prove soficity for this family of groups under a flexible technical hypothesis for $H$ called $σ$-co-sofic. This proves soficity for group doubles $*_H G$, where $H<G$ is an arbitrary separable subgroup and $G$ is countable and sofic. This includes arbitrary finite index group doubles of sofic groups among various other examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_11724 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On soficity for certain fundamental groups of graphs of groups Gao, David Elayavalli, Srivatsav Kunnawalkam Mj, Mahan Group Theory Operator Algebras In this note we study a family of graphs of groups over arbitrary base graphs where all vertex groups are isomorphic to a fixed countable sofic group $G$, and all edge groups $H<G$ are such that the embeddings of $H$ into $G$ are identical everywhere. We prove soficity for this family of groups under a flexible technical hypothesis for $H$ called $σ$-co-sofic. This proves soficity for group doubles $*_H G$, where $H<G$ is an arbitrary separable subgroup and $G$ is countable and sofic. This includes arbitrary finite index group doubles of sofic groups among various other examples. |
| title | On soficity for certain fundamental groups of graphs of groups |
| topic | Group Theory Operator Algebras |
| url | https://arxiv.org/abs/2408.11724 |