We show that the number of monochromatic solutions of the equation x_1^{\alpha_1}x_2^{\alpha_2}\cdots x_r^{\alpha_r}=g in a 2 -coloring of a finite group G , where \alpha_1,\ldots,\alpha_r are permutations and g\in G , depends only on the cardinalities of the chromatic classes but not on their distribution. We give some applications to arithmetic Ramsey statements.