# Ramsey-product subsets of a group

Author
Ivan Franko National University of L'viv, Lviv, Ukraine; Faculty of Computer Science and Cybernetics, Kyiv University, Kyiv, Ukraine
Abstract
Given an infinite group $G$ and a number vector $\overrightarrow{m}=(m_{1},\ldots , m_{k} )\in\mathbb{Z}^{k}$ of finite length $k$, we say that a subset $A$ of $G$ is a Ramsey $\overrightarrow{m}$-product set if every infinite subset $X\subset G$ contains distinct elements $x_{1},\ldots, x_{k} \in X$ such that $x^{m_{1}} _{\sigma(1)}\ldots x^{m_{k}} _{\sigma(k)} \in A$ for any permutation $\sigma\in S_{k}$. We use these subsets to characterize combinatorially some algebraically defined subsets of the Stone-Cech compactification $\beta G$ of $G$.
Keywords
Stone-Cech compactification; product of ultrafilters; Ramsey product subset
DOI
doi:10.15330/ms.47.2.145-149
Reference
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Pages
145-149
Volume
47
Issue
2
Year
2017
Journal
Matematychni Studii
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