Monochromatic Regular Polygons in finitely colored Z2 *Z2 *Z2

Abstract

We show that for any finite coloring of the group Z2 *Z2 *Z2 and for any positive integer k, there always exists a monochromatic regular k-gon in Z2 *Z2 *Z2 with respect to the word length metric induced by the standard generating set; the edge length of which is estimated.

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