Ramsey theory for p-quasicyclic groups with a view towards topological dynamics
Abstract
We prove additive and multiplicative partition theorems, obtaining combinatorial results for p-quasicyclic groups, where p is a prime number. We also get density results for p-quasicyclic groups via left F{\o}lner sequences of non-empty finite subsets of it, giving a sufficient condition in order a subset of a p-quasicyclic group to contain arbitrary long arithmetic progressions. Finally, we introduce the notion of a dynamical system over p-quasicyclic groups extending the classical notion of a topological dynamical system and we prove (multiple) recurrent results for the p-quasicyclic groups. In particular, we prove recurrent results analogous to Furstenberg-Weiss type theorems for classical systems.
Keywords
Cite
@article{arxiv.1212.3520,
title = {Ramsey theory for p-quasicyclic groups with a view towards topological dynamics},
author = {Andreas Koutsogiannis},
journal= {arXiv preprint arXiv:1212.3520},
year = {2014}
}
Comments
26 pages. arXiv admin note: substantial text overlap with arXiv:1101.3226 This paper has been withdrawn by the author for further research