Monochrome symmetric subsets of colored groups

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• 作者：Yuliya Gryshko and Anatole Khelif
• 关键词：Coloring ; Monochromatic ; Group ; Symmetric
• 刊名：Journal of Combinatorial Theory, Series A
• 出版年：2005
• 出版时间：2005
• 年：2005
• 卷：112
• 期：2
• 页码：212-221
• 全文大小：149 K

文摘

In (Electron. J. Combin. 10 (2003); http://www.combinatorics.org/volume-10/Abstracts/v1oi1r28.html), the first author (Yuliya Gryshko) asked three questions. Is it true that every infinite group admitting a 2-coloring without infinite monochromatic symmetric subsets is either almost cyclic (i.e., have a finite index subgroup which is cyclic infinite) or countable locally finite? Does every infinite group G include a monochromatic symmetric subset of any cardinal <|G| for any finite coloring? Does every uncountable group G such that |B(G)|< |G| where B(G)={xG:x²