  Spaces in the genus of infinite quaternionic projective space which admit
essential maps from infinite complex projective space are classified. In these
cases the sets of homotopy classes of maps are described explicitly. These
results strengthen the classical theorem of McGibbon and Rector on maximal
torus admissibility for spaces in the genus of infinite quaternionic projective
space. An interpretation of these results in the context of Adams-Wilkerson
embedding in integral $K$-theory is also given.
