Abstract
The explicit formula for the distortion function of a connected Lie subgroup in a connected simply connected nilpotent Lie group is obtained. In particular, we prove that a function f: N → R can be realized (up to equivalence) as the distortion function of a connected Lie subgroup in a connected simply connected nilpotent Lie group if and only if f ∼ nr for some nonnegative r ∈ Q. Considering lattices in Lie groups, we establish the analogous results for finitely generated nilpotent groups.
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