A remark on the restriction map in field formation

Abstract:

In this note we point out that in a field formation $(G,\{ {G_F}\} ,A)$, if ${h_2}(K/F) = {[K:F]^c}$ for every normal layer $K/F$ with a fixed integer $c \geqslant 0$, then for every tower $F \subset E \subset K$ with $K/F$ normal, the restriction map ${H^2}(K/F) \to {H^2}(K/E)$ is surjective, and give an example with $c = 2$.