David Gao, Srivatsav Kunnawalkam Elayavalli, Mahan Mj
{"title":"关于群的图的某些基群的soficity","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":"{\"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}","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}
On soficity for certain fundamental groups of graphs of groups
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