nilprogression

nil +‎ progression

nilprogression (plural nilprogressions)

1. (mathematics) A function of the products of the elements of a nilpotent group and their inverses
   • 2015, Terence Tao, “Inverse theorems for sets and measures of polynomial growth”, in arXiv‎:

     We give a structural description of the finite subsets ${\displaystyle A}$ of an arbitrary group ${\displaystyle G}$ which obey the polynomial growth condition ${\displaystyle }$ for some bounded ${\displaystyle d}$ and sufficiently large ${\displaystyle n}$, showing that such sets are controlled by (a bounded number of translates of) a coset nilprogression in a certain precise sense.