论文标题
自由因素和完善的
Free factors and profinite completions
论文作者
论文摘要
一个人可以通过其完善的完成群体检测免费的产品吗？我们在几乎免费的小组中积极回答。更确切地说，我们证明，有限生成的几乎免费的组$ g $的子组是自由因素，并且仅当其在$ g $完成$ g $的情况下关闭是一个自由因素。这是Parzanchevski和Puder（后来也由Wilton证明）的自由团体的总体结果。我们的方法与它们的方法完全不同，将概述基团的同源特性和鸡巴和邓伍德的分解理论结合在一起。
Can one detect free products of groups via their profinite completions? We answer positively among virtually free groups. More precisely, we prove that a subgroup of a finitely generated virtually free group $G$ is a free factor if and only if its closure in the profinite completion of $G$ is a profinite free factor. This generalises results by Parzanchevski and Puder (later also proved by Wilton) for free groups. Our methods are entirely different to theirs, combining homological properties of profinite groups and the decomposition theory of Dicks and Dunwoody.
