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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
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
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
Linking options:
https://www.mathnet.ru/eng/mzm4890https://doi.org/10.4213/mzm4890 https://www.mathnet.ru/eng/mzm/v85/i4/p516
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