  A detailed standard model (SM) calculation of the O(alpha_s) virtual
corrections to the decay width for b -> s g is presented (g denotes a gluon).
Also the complete expressions for the corresponding bremsstrahlung corrections
are given. Taking into account the existing next-to-leading logarithmic (NLL)
result for the Wilson coefficient C_8^eff, a complete NLL result for the
branching ratio BR(b->sg) is derived. Numerically, we obtain BR(b->sg)=(5.0 +/-
1.0) * 10^(-3), which is more than a factor of two larger than the leading
logarithmic result. The impact of these corrections on the inclusive charmless
hadronic branching ratio of B-mesons, which can be used to extract
|V_(ub)/V_(cb)|, is shown to be of similar importance as NLL corrections to
b-quark decay modes with three quarks in the final state. Finally, the impact
of the NLL corrections to b->sg on the charmless hadronic branching ratio is
investigated in scenarios, where the Wilson coefficient C_8 is enhanced by new
physics.
