Phantom Maps and Monoids of Endomorphisms of <i>K</i>(<b><i>Z</i></b>,<i>m</i>) x <i>Sⁿ</i>

Abstract

The compositions hf, hg of phantom pair f, g and a phantom map h are homotopic. The compositions hf, kf of phantom pair h, k and a phantom map f are homotopic. We determine the homotopy set [K(Z,m) x Sn, K(Z,m) x Sn] and its monoid structure given by the composition of maps for all m, n ≥ 1.