RESEARCH ANNOUNCEMENT: THE STRUCTURE OF GROUPS WITH A QUASICONVEX HIERARCHY

Q3 Mathematics

Electronic Research Announcements in Mathematical Sciences Pub Date : 2009-10-01 DOI:10.3934/ERA.2009.16.44

D. Wise

引用次数: 342

Abstract

Let $G$ be a word-hyperbolic group with a quasiconvex hierarchy. We show that $G$ has a finite index subgroup $G'$ that embeds as a quasiconvex subgroup of a right-angled Artin group. It follows that every quasiconvex subgroup of $G$ is a virtual retract, and is hence separable. The results are applied to certain 3-manifold and one-relator groups.

查看原文本刊更多论文

研究公告:具有拟凸层次的群的结构

设$G$是一个具有拟凸层次的词双曲群。证明了$G$有一个有限索引子群$G'$，它嵌入为直角Artin群的拟凸子群。由此得出$G$的每一个拟凸子群都是虚缩回，因此是可分的。结果应用于某些3流形和1相关群。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Electronic Research Announcements in Mathematical Sciences 数学-数学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Electronic Research Archive (ERA), formerly known as Electronic Research Announcements in Mathematical Sciences, rapidly publishes original and expository full-length articles of significant advances in all branches of mathematics. All articles should be designed to communicate their contents to a broad mathematical audience and must meet high standards for mathematical content and clarity. After review and acceptance, articles enter production for immediate publication. ERA is the continuation of Electronic Research Announcements of the AMS published by the American Mathematical Society, 1995—2007