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 G n with coefficients in F [ w ± 1 ] to the cohomology of G n + 1 with coefficients in the graded field F ( ( u n ) ) [ u ± 1 ] . In this note we study the behavior of Θ on H 1 . Then it is shown that Θ is injective on H 1 for n ⩾ 1 and for all primes p.