Duke Mathematical Journal

Piecewise automatic groups

Anna Erschler

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Abstract

We introduce a notion of a piecewise automatic group. Among these groups we describe a new class of groups of intermediate growth. We show that for any function f:NN, there exists a finitely generated torsion group of intermediate growth G for which the Følner function satisfies FølG,S(n)f(n) for some generating set S and all sufficiently large n. As a corollary we see that the asymptotic entropy of simple random walks on these groups could be arbitrarily close to being linear, while the Poisson boundary is trivial

Article information

Source
Duke Math. J., Volume 134, Number 3 (2006), 591-613.

Dates
First available in Project Euclid: 28 August 2006

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1156771904

Digital Object Identifier
doi:10.1215/S0012-7094-06-13435-X

Mathematical Reviews number (MathSciNet)
MR2254627

Zentralblatt MATH identifier
1159.20019

Subjects
Primary: 20F65: Geometric group theory [See also 05C25, 20E08, 57Mxx] 20F69: Asymptotic properties of groups 20E08: Groups acting on trees [See also 20F65] 60B15: Probability measures on groups or semigroups, Fourier transforms, factorization
Secondary: 20F05: Generators, relations, and presentations 20F50: Periodic groups; locally finite groups

Citation

Erschler, Anna. Piecewise automatic groups. Duke Math. J. 134 (2006), no. 3, 591--613. doi:10.1215/S0012-7094-06-13435-X. https://projecteuclid.org/euclid.dmj/1156771904


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