Johnson, John H.Richter, Florian Karl2021-11-262021-11-262021-11-262017-12-0110.1016/j.aim.2017.09.033https://infoscience.epfl.ch/handle/20.500.14299/1832541607.05320Answering a question posed by Bergelson and Leibman in [6], we establish a nilpotent version of the Polynomial Hales–Jewett Theorem that contains the main theorem in [6] as a special case. Important to the formulation and the proof of our main theorem is the notion of a relative syndetic set (relative with respect to a closed non-empty subsets of βG) [25]. As a corollary of our main theorem we prove an extension of the restricted van der Waerden Theorem to nilpotent groups, which involves nilprogressions.text::journal::journal article::research article