Uniform non--amenability of free Burnside groups

Details Uniform non--amenability of free Burnside groups Uniform non--amenability of free Burnside groups

2004-04-05

arxiv.org/abs/math/0404073v1

Mathematics

Group Theory

9 pages

Scientific paper

We 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 groups without non--abelian free subgroups. As another consequence, we obtain that the above--mentioned groups are of uniform exponential growth.

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