On relations between 1-lines of Adams-Novikov spectral sequences modulo invariant prime ideals

We have a ring homomorphism Θ from the cohomology of the extended Morava stabilizer group Gn with coefficients in F[w±1] to the cohomology of Gn+1 with coefficients in the graded field F((un))[u±1]. In this note we study the behavior of Θ on H1. Then it is shown that Θ is injective on H1 for n⩾1 and for all primes p.