Monochrome Symmetric Subsets in 2-Colorings of Groups - Gryshko, Yuliya (The Electronic Journal of Combinatorics, 2003)
A subset A of a group G is called symmetric with respect to the element gG if A=gA^-1g. It is proved that in any 2-coloring, every infinite group G contains monochrome symmetric subsets of arbitrarily large cardinality < |G|.