David Gao, Srivatsav Kunnawalkam Elayavalli, Mahan Mj
{"title":"On soficity for certain fundamental groups of graphs of groups","authors":"David Gao, Srivatsav Kunnawalkam Elayavalli, Mahan Mj","doi":"arxiv-2408.11724","DOIUrl":null,"url":null,"abstract":"In this note we study a family of graphs of groups over arbitrary base graphs\nwhere all vertex groups are isomorphic to a fixed countable sofic group $G$,\nand all edge groups $H<G$ are such that the embeddings of $H$ into $G$ are\nidentical everywhere. We prove soficity for this family of groups under a\nflexible technical hypothesis for $H$ called $\\sigma$-co-sofic. This proves\nsoficity for group doubles $*_H G$, where $H<G$ is an arbitrary separable\nsubgroup and $G$ is countable and sofic. This includes arbitrary finite index\ngroup doubles of sofic groups among various other examples.","PeriodicalId":501114,"journal":{"name":"arXiv - MATH - Operator Algebras","volume":"14 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Operator Algebras","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.11724","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
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