A nilpotent Freiman dimension lemma
  We prove that a K-approximate subgroup of an arbitrary torsion-free nilpotent group can be covered by a bounded number of cosets of a nilpotent subgroup of bounded rank, where the bounds are explicit and depend only on K. The result can be seen as a nilpotent analogue to Freiman's dimension lemma. 
Emmanuel Breuillard, Ben Green and Terence Tao
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