Uniform non-amenability of free Burnside groups
نویسندگان
چکیده
منابع مشابه
Uniform Non–amenability of Free Burnside Groups
The aim of the present note is to show that free Burnside groups of sufficiently large odd exponent are non–amenable in a certain strong sense, more precisely, their left regular representations are isolated from the trivial representation uniformly on finite generating sets. This result is applied to the solution of a strong version of the von Neumann – Day problem concerning amenability of gr...
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In this paper, we study some properties of the outer automorphism group of free Burnside groups of large odd exponent. In particular, we prove that it contains free and free abelian subgroups.
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We prove that any maximal group in the free Burnside semi-group deened by the equation x n = x n+m for any n 1 and any m 1 is a free Burnside group satisfying x m = 1. We show that such group is free over a well described set of generators whose cardinality is the cyclomatic number of a graph associated to the J-class containing the group. For n = 2 and for every m 2 we present examples with 2m...
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We construct an embedding of a free Burnside group B(m, n) of odd n > 2 and rank m > 1 in a finitely presented group with some special properties. The main application of this embedding is an easy construction of finitely presented non-amenable groups without noncyclic free subgroups (which provides a finitely presented counterexample to the von Neumann problem on amenable groups). As another a...
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ژورنال
عنوان ژورنال: Archiv der Mathematik
سال: 2007
ISSN: 0003-889X,1420-8938
DOI: 10.1007/s00013-006-2002-5