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Dec 17, 2014 at 16:25 comment added HJRW That should be undistorted. Anyway, mapping tori of suitable automorphisms of $\mathbb{Z}^{n+1}$ should give examples for any $n$.
Dec 16, 2014 at 22:25 comment added HJRW What about lattices in Sol? I think their cyclic subgroups are in distorted.
Dec 16, 2014 at 16:21 history asked Seirios CC BY-SA 3.0