On $\mathrm {hom} \dim M \mathrm {U}_* (X\times Y)$

Abstract:

Let $p$ be a prime and $B{\mathbf {Z}}/p$ the classifying space for the cyclic group ${\mathbf {Z}}/p$ of prime order $p$. A finite complex $X$ is constructed such that \[ \hom \cdot {\dim _{M{U_ \ast }}}M{U_ \ast }(X \times B{\mathbf {Z}}/p) > \hom \cdot {\dim _{M{U_ \ast }}}M{U_ \ast }(X) + \hom \cdot {\dim _{M{U_ \ast }}}M{U_ \ast }(B{\mathbf {Z}}/p).\]