On soficity for certain fundamental groups of graphs of groups
Abstract
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 $\sigma$-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.
- Publication:
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arXiv e-prints
- Pub Date:
- August 2024
- DOI:
- 10.48550/arXiv.2408.11724
- arXiv:
- arXiv:2408.11724
- Bibcode:
- 2024arXiv240811724G
- Keywords:
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- Mathematics - Group Theory;
- Mathematics - Operator Algebras