论文标题
免费产品旋转和旋转家庭
Free products from spinning and rotating families
论文作者
论文摘要
Dahmani-Guirardel-Osin和Clay-Mangahas-Margalit的最新作品的深远工作为几何方法提供了研究在环境组$ G $中的正常关闭（或亚组集合）的正常关闭的方法。他们的工作提供了条件，$ g $中的正常关闭是免费产品。在本文中，我们统一了他们的结果，并简化并大大缩短了大体甲基甲烷定理的证明。
The far-reaching work of Dahmani-Guirardel-Osin and recent work of Clay-Mangahas-Margalit provide geometric approaches to the study of the normal closure of a subgroup (or a collection of subgroups)in an ambient group $G$. Their work gives conditions under which the normal closure in $G$ is a free product. In this paper we unify their results and simplify and significantly shorten the proof of the Dahmani-Guirardel-Osin theorem.
