  We compute the one-loop electroweak Sudakov corrections to the production
process Z (nu bar{nu}) + n jets, with n = 1,2,3, in p p collisions at the LHC.
It represents the main irreducible background to new physics searches at the
energy frontier. The results are obtained at the leading and next-to-leading
logarithmic accuracy by implementing the general algorithm of Denner-Pozzorini
in the event generator for multiparton processes ALPGEN. For the standard
selection cuts used by ATLAS and CMS collaborations, we show that the Sudakov
corrections to the relevant observables can grow up to - 40% at sqrt{s} = 14
TeV. We also include the contribution due to undetected real radiation of
massive gauge bosons, to show to what extent the partial cancellation with the
large negative virtual corrections takes place in realistic event selections.
