nilprogression

English

Etymology

nil +‎ progression

Noun

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^[1]:

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