Geodesic
Monochrome symmetric subsets in \(2\)-colorings of groups
The electronic journal of combinatorics, Tome 10 (2003)
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A subset $A$ of a group $G$ is called symmetric with respect to the element $g\in G$ if $A=gA^{-1}g$. It is proved that in any 2-coloring, every infinite group $G$ contains monochrome symmetric subsets of arbitrarily large cardinality $ < |G|$.
DOI : 10.37236/1721
Classification : 05D10, 20B07 
@article{10_37236_1721,
     author = {Yuliya Gryshko},
     title = {Monochrome symmetric subsets in \(2\)-colorings of groups},
     journal = {The electronic journal of combinatorics},
     year = {2003},
     volume = {10},
     doi = {10.37236/1721},
     zbl = {1023.05132},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1721/}
}
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DO  - 10.37236/1721
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%0 Journal Article
%A Yuliya Gryshko
%T Monochrome symmetric subsets in \(2\)-colorings of groups
%J The electronic journal of combinatorics
%D 2003
%V 10
%U http://geodesic.mathdoc.fr/articles/10.37236/1721/
%R 10.37236/1721
%F 10_37236_1721
Yuliya Gryshko. Monochrome symmetric subsets in \(2\)-colorings of groups. The electronic journal of combinatorics, Tome 10 (2003). doi: 10.37236/1721

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