A nilpotent Freiman dimension lemma

Abstract

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.

8 pages, submitted to special volume of EJC in honour of Yahya Ould Hamidoune