Amenability of linear-activity automaton groups

Gideon Amir; Omer Angel; Balint Virag

doi:10.4171/JEMS/373

Amenability of linear-activity automaton groups

Gideon Amir, Omer Angel, Balint Virag

Department of Mathematics

Bar-Ilan University

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

Abstract

We prove that every linear-activity automaton group is amenable. The proof is based on showing that a random walk on a specially constructed degree 1 automaton group-the mother group-has asymptotic entropy 0. Our result answers an open question by Nekrashevych in the Kourovka notebook, and gives a partial answer to a question of Sidki.

Original language	English
Pages (from-to)	705-730
Number of pages	26
Journal	Journal of the European Mathematical Society
Volume	15
Issue number	3
DOIs	https://doi.org/10.4171/JEMS/373
State	Published - 2013

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

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10.4171/JEMS/373

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title = "Amenability of linear-activity automaton groups",

abstract = "We prove that every linear-activity automaton group is amenable. The proof is based on showing that a random walk on a specially constructed degree 1 automaton group-the mother group-has asymptotic entropy 0. Our result answers an open question by Nekrashevych in the Kourovka notebook, and gives a partial answer to a question of Sidki.",

author = "Gideon Amir and Omer Angel and Balint Virag",

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AU - Virag, Balint

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AB - We prove that every linear-activity automaton group is amenable. The proof is based on showing that a random walk on a specially constructed degree 1 automaton group-the mother group-has asymptotic entropy 0. Our result answers an open question by Nekrashevych in the Kourovka notebook, and gives a partial answer to a question of Sidki.

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U2 - 10.4171/JEMS/373

DO - 10.4171/JEMS/373

M3 - مقالة

SN - 1435-9855

VL - 15

SP - 705

EP - 730

JO - Journal of the European Mathematical Society

JF - Journal of the European Mathematical Society

IS - 3

ER -

Amenability of linear-activity automaton groups

Abstract

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