  We study the existence of transformations of the transfinite plane that allow
one to reduce Ramsey-theoretic statements concerning uncountable Abelian groups
into classical partition relations for uncountable cardinals.
  To exemplify: we prove that for every inaccessible cardinal $\kappa$, if
$\kappa$ admits a stationary set that does not reflect at inaccessibles, then
the classical negative partition relation $\kappa\nrightarrow[\kappa]^2_\kappa$
implies that for every Abelian group $(G,+)$ of size $\kappa$, there exists a
map $f:G\rightarrow G$ such that, for every $X\subseteq G$ of size $\kappa$ and
every $g\in G$, there exist $x\neq y$ in $X$ such that $f(x+y)=g$.
