Monochromatic Regular Polygons in finitely colored ${\mathbb{Z}}_2\ast {\mathbb{Z}}_2\ast {\mathbb{Z}}_2$

Hui Xu, Enhui Shi

We show that for any finite coloring of the group ${\mathbb{Z}}_2\ast {\mathbb{Z}}_2\ast {\mathbb{Z}}_2$ and for any positive integer $k$, there always exists a monochromatic regular $k$-gon i…