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arXiv · 1212.3520

Ramsey theory for p-quasicyclic groups with a view towards topological dynamics

Andreas Koutsogiannis
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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 Følner 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.

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Andreas Koutsogiannis. 2014-08-17. Ramsey theory for p-quasicyclic groups with a view towards topological dynamics. https://arxiv.org/abs/1212.3520

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