  For a locally compact abelian group $G$, J. L. Taylor (1971) gave a complete
characterization of invertible elements in the measure algebra $M(G)$. Using
the Fourier-Stieltjes transform, this characterization can be carried out in
the context of Fourier-Stieltjes algebras $B(G)$. We obtain this latter
characterization for the Fourier-Stieltjes algebra $B(G)$ of certain classes of
locally compact groups, in particular, many totally minimal groups and the
$ax+b$-group.
