On the restriction map of the Fourier-Stieltjes algebra B(G) and Bp(G)

G is a locally compact group that contains the semidirect product J of a closed normal subgroup H and a closed connected subgroup K. Conditions on J are given that imply that the restriction map B_p(G) → B_p(H) (1 < p < ∞; G amenable if p ≠ 2) of the Fourier-Stieltjes algebras is not surjective. It is also shown that if the restriction map B(J) → B(H) is surjective, J need not be a direct product, even if H is nilpotent.