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Matematicheskie Zametki, 2009, Volume 85, Issue 4, Pages 516–523
DOI: https://doi.org/10.4213/mzm4890
(Mi mzm4890)
 

This article is cited in 17 scientific papers (total in 17 papers)

Uniform Nonamenability of Subgroups of Free Burnside Groups of Odd Period

V. S. Atabekyan

Yerevan State University
References:
Abstract: A famous theorem of Adyan states that, for any $m\ge 2$ and any odd $n\ge 665$, the free $m$-generated Burnside group $B(m,n)$ of period $n$ is not amenable. It is proved in the present paper that every noncyclic subgroup of the free Burnside group $B(m,n)$ of odd period $n\ge 1003$ is a uniformly nonamenable group. This result implies the affirmative answer, for odd $n\ge 1003$, to the following de la Harpe question: Is it true that the infinite free Burnside group $B(m,n)$ has uniform exponential growth? It is also proved that every $S$-ball of radius $(400n)^3$ contains two elements which form a basis of a free periodic subgroup of rank 2 in $B(m,n)$, where $S$ is an arbitrary set of elements generating a noncyclic subgroup of $B(m,n)$.
Keywords: free Burnside group, periodic group, amenable group, uniformly nonamenable groups, Følner constant, uniform exponential growth, hyperbolic group.
Received: 22.04.2008
Revised: 30.06.2008
English version:
Mathematical Notes, 2009, Volume 85, Issue 4, Pages 496–502
DOI: https://doi.org/10.1134/S0001434609030213
Bibliographic databases:
UDC: 512.543
Language: Russian
Citation: V. S. Atabekyan, “Uniform Nonamenability of Subgroups of Free Burnside Groups of Odd Period”, Mat. Zametki, 85:4 (2009), 516–523; Math. Notes, 85:4 (2009), 496–502
Citation in format AMSBIB
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\paper Uniform Nonamenability of Subgroups of Free Burnside Groups of Odd Period
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\yr 2009
\vol 85
\issue 4
\pages 516--523
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\jour Math. Notes
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  • This publication is cited in the following 17 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Математические заметки Mathematical Notes
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