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We report on the calculation of the factorisable one-loop weak-interactioncorrections to the initial and final states for three-jet observables inelectron-positron annihilations. We show that such corrections are of a fewpercent at $\sqrt s=M_Z$. Hence, while their impact is not dramatic in thecontext of LEP1 and SLC, where the total error on the measured value of$\alpha_{\mathrm{S}}$ is larger, at a future Linear Collider, running at the$Z$ mass peak (e.g., GigaZ), they ought to be taken into account in theexperimental fits, as here the uncertainty on the value of the strong couplingconstant is expected to be at the 0.1% level or even smaller. The calculationhas been performed using helicity amplitudes so that it can be applied to thecase of polarised beams.Comment: 22 pages, latex, 7 figures (substantial revisions, version to be  published in JHEP

Weak corrections to three-jet production in electron-positron annihilations, 1. The factorisable contributions