Rational embeddings of hyperbolic groups

Belk James; Bleak Collin; Matucci Francesco

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Rational embeddings of hyperbolic groups

机译：合理的嵌入的双曲组

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摘要

We prove that all Gromov hyperbolic groups embed into the asynchronous rational group defined by Grigorchuk, Nekrashevych and Sushchanski.i. The proof involves assigning a system of binary addresses to points in the Gromov boundary of a hyperbolic group G, and proving that elements of G act on these addresses by asynchronous transducers. These addresses derive from a certain self-similar tree of subsets of G, whose boundary is naturally homeomorphic to the horofunction boundary of G.

机译：我们证明所有格罗莫夫双曲组嵌入异步rational组织定义的证据包括分配系统的二进制地址的格罗莫夫边界点双曲G组,证明的元素异步G作用于这些地址传感器。某些自相似的子集树G的边界的自然是同胚的horofunction G的边界。

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来源
《Journal of combinatorial algebra》 |2021年第2期|123-183|共61页
作者
Belk James; Bleak Collin; Matucci Francesco;
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作者单位

Univ Milano Bicocca, Dipartimento Matemat & Applicaz, I-20125 Milan, Italy;

Univ St Andrews, Sch Math & Stat, St Andrews KY16 9SS, Fife, Scotland;

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正文语种英语
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关键词
Rational number; Proof; HyperbolicBoundaryTransducersAsynchronous;

机译：有理数;证据;HyperbolicBoundaryTransducer;

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Rational embeddings of hyperbolic groups

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