标题： 关于某些图群的基本群的软性 显示英文标题

标题： On soficity for certain fundamental groups of graphs of groups

摘要： 在本文中，我们研究了一类图的群，其基础图是任意的，其中所有顶点群都同构于一个固定的可数软群$G$，所有边群$H<G$都满足$H$到$G$的嵌入在所有地方都是相同的。 我们在对$H$的一个灵活的技术假设下证明了这个群族的软性，该假设称为$\sigma$-co-软。 这证明了群双倍$*_H G$的sofic性，其中$H<G$是一个任意的可分子群，$G$是可数且sofic的。 这包括各种其他例子中的sofic群的任意有限指数群双倍。 显示英文摘要

摘要： 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.