For complex orientations preserving power operations, p-typicality is atypical

We show, for primes p⩽13, that a number of well-known MU(p)-rings do not admit the structure of commutative MU(p)-algebras. These spectra have complex orientations that factor through the Brown–Peterson spectrum and correspond to p-typical formal group laws. We provide computations showing that such a factorization is incompatible with the power operations on complex cobordism. This implies, for example, that if E is a Landweber exact MU(p)-ring whose associated formal group law is p-typical of positive height, then the canonical map MU(p)→E is not a map of H∞ ring spectra. It immediately follows that the standard p-typical orientations on BP,E(n), and En do not rigidify to maps of E∞ ring spectra. We conjecture that similar results hold for all primes.