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Rational embeddings of hyperbolic groups
- Publication Year :
- 2021
-
Abstract
- We prove that all Gromov hyperbolic groups embed into the asynchronous rational group defined by Grigorchuk, Nekrashevych and Sushchanskiǐ. 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.
Details
- Database :
- OAIster
- Notes :
- STAMPA, English
- Publication Type :
- Electronic Resource
- Accession number :
- edsoai.on1308942101
- Document Type :
- Electronic Resource