The homotopy groups of a space are endowed with homotopy operations which define the Pi-algebra of the space. An Eilenberg-MacLane space is the realization of a Pi-algebra concentrated in one degree. In this paper, we provide necessary and sufficient conditions for the realizability of a Pi-algebra concentrated in two degrees. We then specialize to the stable case, and list infinite families of such Pi-algebras that are not realizable.
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