# Kaleidoscopical configurations in groups

Author I. V. Protasov, S. Slobodianiuk
i.v.protasov@gmail.com, slobodianiuk@yandex.ru
Kyiv Taras Shevchenko University

Abstract A subset $A$ of a group $G$ is called a kaleidoscopical configuration if there exists a surjective coloring $\chi\colon X\rightarrow \kappa$ such that the restriction $\chi|gA$ is a bijection for each $g\in G$. We give two topological constructions of kaleidoscopical configurations and show that each infinite subset of an Abelian group contains an infinite kaleidoscopical configuration.
Keywords kaleidoscopical configuration; T-sequence; rigid subset
Reference 1. T. Banakh, I. Protasov, Zariski topologies on groups, preprint available in ArXiv:1001.0601.

2. T. Banakh, O. Petrenko, I. Protasov, S. Slobodianiuk, Kaleidoscopical configurations in G-spaces, available in ArXiv:1001.0903.

3. I. Protasov, E. Zelenyuk, Topologies on Groups Determined by Sequences, Math. Stud. Monogr. Ser., V.4, VNTL Publisher, Lviv, 1999.

4. I. Protasov, K. Protasova, Kaleidoscopical Graphs and Hamming codes, Voronoi’s Impact on Modern Science, Book 4, V.1, Proc. 4th Intern. Conf. on Analytic Number Theory and Spatial Tesselations, Institute of Mathematics, NAS of Ukraine, Kyiv, 2008, 240–245.

5. E. Zelenyuk, Topologization of groups, J. Group Theory, 10 (2007), 235–244.

Pages 115-118
Volume 36
Issue 2
Year 2011
Journal Matematychni Studii
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