In 1976, Nickolas showed that for each natural n, the free topological group \(F(X^n)\) is topologically isomorphic to a subgroup of F(X) provided X is a compact space or, more generally, a \(k_{\omega }\) -space. We complement the Nickolas’ embedding theorem by showing that it remains true for every topological space X such that all finite powers of X are pseudocompact. For example, all pseudocompact k-spaces enjoy this property. Also, we extend the embedding theorem to the class of \(NC_\omega \) -spaces that includes, in particular, the \(k_\omega \) -spaces and the well-ordered spaces of ordinals \([0, \alpha )\) , for every ordinal \(\alpha \) . Our results are quite sharp because we present a first example of a Tychonoff space Z such that F(Z) does not contain an isomorphic copy of the group \(F(Z^2)\) . In addition, our space Z is countably compact, separable, and its square \(Z^2\) is not pseudocompact.
