An example of a 36-Shelah group

A group $G$ is called $n$-Shelah if $G=A^n$ for any subset $A\subseteq G$ of cardinality $|A|=|G|$. In 1980 Saharon Shelah constructed his famous CH-example of an uncountable 6640-Shelah group. This group was the first example of a nontopologizable group. On the other hand, by a result of Protasov, every countable $n$-Shelah group is finite and by a result of Cornullier, every 3-Shelah group is finite. Modifying the approach of Shelah, we shall construct a CH-example of a 36-Shelah group possessing some additional interesting (for Topological Algebra) properties. We do not know what happens with n-Shelah groups for 3<n<36.