Growth of quasiconvex subgroups

François Dahmani; David Futer; Daniel T. Wise

doi:10.1017/S0305004118000440

Growth of quasiconvex subgroups

François Dahmani, David Futer, Daniel T. Wise

Research output: Contribution to journal › Article › peer-review

Abstract

We prove that non-elementary hyperbolic groups grow exponentially more quickly than their infinite index quasiconvex subgroups. The proof uses the classical tools of automatic structures and Perron-Frobenius theory. We also extend the main result to relatively hyperbolic groups and cubulated groups. These extensions use the notion of growth tightness and the work of Dahmani, Guirardel and Osin on rotating families.

Original language	English
Pages (from-to)	505-530
Number of pages	26
Journal	Mathematical Proceedings of the Cambridge Philosophical Society
Volume	167
Issue number	3
DOIs	https://doi.org/10.1017/S0305004118000440
State	Published - 1 Nov 2019
Externally published	Yes

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1017/S0305004118000440

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title = "Growth of quasiconvex subgroups",

abstract = "We prove that non-elementary hyperbolic groups grow exponentially more quickly than their infinite index quasiconvex subgroups. The proof uses the classical tools of automatic structures and Perron-Frobenius theory. We also extend the main result to relatively hyperbolic groups and cubulated groups. These extensions use the notion of growth tightness and the work of Dahmani, Guirardel and Osin on rotating families.",

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year = "2019",

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AU - Dahmani, François

AU - Futer, David

AU - Wise, Daniel T.

PY - 2019/11/1

Y1 - 2019/11/1

N2 - We prove that non-elementary hyperbolic groups grow exponentially more quickly than their infinite index quasiconvex subgroups. The proof uses the classical tools of automatic structures and Perron-Frobenius theory. We also extend the main result to relatively hyperbolic groups and cubulated groups. These extensions use the notion of growth tightness and the work of Dahmani, Guirardel and Osin on rotating families.

AB - We prove that non-elementary hyperbolic groups grow exponentially more quickly than their infinite index quasiconvex subgroups. The proof uses the classical tools of automatic structures and Perron-Frobenius theory. We also extend the main result to relatively hyperbolic groups and cubulated groups. These extensions use the notion of growth tightness and the work of Dahmani, Guirardel and Osin on rotating families.

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DO - 10.1017/S0305004118000440

M3 - مقالة

SN - 0305-0041

VL - 167

SP - 505

EP - 530

JO - Mathematical Proceedings of the Cambridge Philosophical Society

JF - Mathematical Proceedings of the Cambridge Philosophical Society

IS - 3

ER -

Growth of quasiconvex subgroups

Abstract

All Science Journal Classification (ASJC) codes

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