Free groups of interval exchange transformations are rare

Details Free groups of interval exchange transformations are rare Free groups of interval exchange transformations are rare

2011-01-31

arxiv.org/abs/1101.5909v2

Mathematics

Group Theory

24 pages

Scientific paper

We study the group IET of all interval exchange transformations. Our first main result is that the group generated by a generic pairs of elements of IET is not free (assuming a suitable irreducibility condition on the underlying permutation). Then we prove that any connected Lie group isomorphic to a subgroup of IET is abelian. Additionally, we show that IET contains no infinite Kazhdan group. We also prove residual finiteness of finitely presented subgroups of IET and give an example of a two-generated subgroup of IET of exponential growth that contains an isomorphic copy of every finite group, and which is therefore not linear.

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