Revisiting the nilpotent polynomial Hales–Jewett theorem

John H. Johnson*, Florian Karl Richter

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Answering 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.

Original languageEnglish (US)
Pages (from-to)269-286
Number of pages18
JournalAdvances in Mathematics
Volume321
DOIs
StatePublished - Dec 1 2017

Keywords

  • Algebra in the Stone–Čech compactification
  • Nilpotent groups
  • Nilprogressions
  • Polynomial Hales–Jewett Theorem
  • Ramsey theory
  • Syndetic sets

ASJC Scopus subject areas

  • Mathematics(all)

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