论文标题
双曲线组的扩展具有局部均匀的指数生长
Extensions of hyperbolic groups have locally uniform exponential growth
论文作者
论文摘要
我们介绍了根据群体定律建模的亚组替代方案的定量表征，并调查何时在扩展下保存该特性。我们开发了一个框架，使我们可以扩展已知具有局部指数增长的组类别，以通过具有局部统一的指数增长的群体来包括单词双曲线或右角ARTIN组的扩展。由此，我们推断出无扭转的单端双曲线群的自动形态群具有局部均匀的指数增长。我们的方法还表明，无扭转的单端摩尔群体相对双曲线组和某些右角artin组的自动形态群体满足我们的定量亚组替代方案。
We introduce a quantitative characterization of subgroup alternatives modeled on the Tits alternative in terms of group laws and investigate when this property is preserved under extensions. We develop a framework that lets us expand the classes of groups known to have locally uniform exponential growth to include extensions of either word hyperbolic or right-angled Artin groups by groups with locally uniform exponential growth. From this, we deduce that the automorphism group of a torsion-free one-ended hyperbolic group has locally uniform exponential growth. Our methods also demonstrate that automorphism groups of torsion-free one-ended toral relatively hyperbolic groups and certain right-angled Artin groups satisfy our quantitative subgroup alternative.
