Groups of given intermediate word growth

Bartholdi, Laurent; Erschler, Anna

doi:10.5802/aif.2902

Cited by 37 publications

(42 citation statements)

References 23 publications

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“…An interesting question informally asked by M. Sapir is whether there exist groups which have oscillating word growth, but non-oscillating conjugacy growth. In particular, one source of examples of groups with oscillating word growth is given by examples of L. Bartholdi and A. Erschler in [6]. Question 1.…”

Section: Grigorchuk Groupmentioning

confidence: 99%

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Conjugacy growth and width of certain branch groups

Fink

2014

Int. J. Algebra Comput.

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The conjugacy growth function counts the number of distinct conjugacy classes in a ball of radius n. We give a lower bound for the conjugacy growth of certain branch groups, among them the Grigorchuk group. This bound is a function of intermediate growth. We further proof that certain branch groups have the property that every element can be expressed as a product of uniformly boundedly many conjugates of the generators. We call this property bounded conjugacy width. We also show how bounded conjugacy width relates to other algebraic properties of groups and apply these results to study the palindromic width of some branch groups.In this section we will recall some of the notation and definitions for branch groups from [8] and [32]. TreesA tree is a connected graph which has no non-trivial cycles. If T has a distinguished root vertex r it is called a rooted tree. The distance of a vertex v from the root is given by the length of the path from r to v and called the norm of v. The number

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Section: Grigorchuk Groupmentioning

confidence: 99%

“…Question 1. Do the groups of oscillating intermediate growth as defined in [6] also have oscillating conjugacy growth?…”

Section: Grigorchuk Groupmentioning

confidence: 99%

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Conjugacy growth and width of certain branch groups

Fink

2014

Int. J. Algebra Comput.

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“…The most general and complete result so far on groups with known intermediate growth rate is the following theorem by L. Bartholdi and A. Erschler [BE11]. Unfortunately, this result is too recent to have been included in [Man12].…”

Section: Book Reviewsmentioning

confidence: 99%

Book Review: How groups grow

Nekrashevych¹

2013

Bull. Amer. Math. Soc.

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“…We would like to point out that intermediate groups satisfying conditions of Corollary 4.2(iv) are shown to exist, see for example [2] and [3].…”

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confidence: 99%

Norm-Controlled Inversion in Weighted Convolution Algebras

Samei

Shepelska

2019

J Fourier Anal Appl

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Let G be a discrete group, let p ≥ 1, and let ω be a weight on G. Using the approach from [9], we provide sufficient conditions on a weight ω for ℓ p (G, ω) to be a Banach algebra admitting a norm-controlled inversion in the reduced C * -algebra of G, namely C * r (G). We show that our results can be applied to various cases including locally finite groups as well as finitely generated groups of polynomial or intermediate growth and a natural class of weights on them. These weights are of the form of polynomial or certain subexponential functions. We also consider the non-discrete case and study the existence of norm-controlled inversion in B(L 2 (G)) for some related convolution algebras.

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Groups of given intermediate word growth

Cited by 37 publications

References 23 publications

Conjugacy growth and width of certain branch groups

Conjugacy growth and width of certain branch groups

Book Review: How groups grow

Norm-Controlled Inversion in Weighted Convolution Algebras

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