  We compute the full one-loop EW contributions of O(\alpha_S alpha_EM^3)
entering the electron-positron into two b-quarks and one gluon cross section at
the Z peak and LC energies. We include both factorisable and non-factorisable
virtual corrections, photon bremsstrahlung but not the real emission of W^\pm
and Z bosons. Their importance for the measurement of alpha_S from jet rates
and shape variables is explained qualitatively and illustrated quantitatively.
Their impact on the forward-backward asymmetry is also analysed.

High Energy Physics - Phenomenology