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Given a topological group $G$ we calculate or evaluate the cardinalcharacteristic $c_k(G)$ (and $c_k^B(G)$) equal to the smallest cardinality of a$k$-centerpole subset $C\subset G$ for (Borel) colorings of $G$. A subset$C\subset G$ of a topological group $G$ is called {\em $k$-centerpole} if foreach (Borel) $k$-coloring of $G$ there is an unbounded monochromatic subset$G$, which is symmetric with respect to a point $c\in C$ in the sense that$S=cS^{-1}c$.

Centerpole sets for colorings of Abelian groups