We prove that the p-universality of a space does not depend on a prime p but only on its rational homotopy type. The minimal model of such a rational homotopy type is characterized by the existence of the trivial endomorphism in the closure of its automorphism group.
Cite this article
R. Body, M. Mimura, Hiroo Shiga, Dennis Sullivan, p-universal spaces and rational homotopy types. Comment. Math. Helv. 73 (1998), no. 3, pp. 427–442