Chromatic numbers and Bohr topologies

We use chromatic numbers of hypergraphs to study the Bohr topology G# on discrete Abelian groups. In particular, if K is an infinite Abelian group of a given prime exponent, we show that G# and K# are homeomorphic iff G is the product of K and some finite group. Also, if K is of finite exponent and G is not of finite exponent, then G# is never topologically embeddable in K#.