# Norm() of bilinear pairing

Consider two points P, Q over a pairing friendly elliptic curve $$E[F_q]$$, e.g., BN254. Let Z = e(P, Q). It is known that $$Z \in F_{q^k}$$ where $$k$$ is the embedding degree. The norm map N(Z) is defined as $$\prod_{0\leq i\leq k-1} Z^{q^i}$$. We observed that for BN254, N(Z) is always the 1 in $$F_p$$.

Is that the case for all pairing friendly groups?