On monochromatic solutions of equations in groups

  • Peter J. Cameron

    Queen Mary University of London, UK
  • Javier Cilleruelo

    Universidad Autónoma de Madrid, Spain
  • Oriol Serra

    Universitat Politècnica de Catalunya, Barcelona, Spain


We show that the number of monochromatic solutions of the equation x1α1x2α2xrαr=gx_1^{\alpha_1}x_2^{\alpha_2}\cdots x_r^{\alpha_r}=g in a 22-coloring of a finite group GG, where α1,,αr\alpha_1,\ldots,\alpha_r are permutations and gGg\in G, depends only on the cardinalities of the chromatic classes but not on their distribution. We give some applications to arithmetic Ramsey statements.

Cite this article

Peter J. Cameron, Javier Cilleruelo, Oriol Serra, On monochromatic solutions of equations in groups. Rev. Mat. Iberoam. 23 (2007), no. 1, pp. 385–395

DOI 10.4171/RMI/499