Searches for the lepton flavour violating decay τ−→μ−μ+μ− and the lepton flavour and baryon number violating decays τ−→p¯μ+μ− and τ−→pμ−μ− have been carried out using proton-proton collision data, corresponding to an integrated luminosity of 1.0 fb−1, taken by the LHCb experiment at s√=7 TeV. No evidence has been found for any signal, and limits have been set at 90% confidence level on the branching fractions: B(τ−→μ−μ+μ−)<8.0×10−8, B(τ−→p¯μ+μ−)<3.3×10−7 and B(τ−→pμ−μ−)<4.4×10−7. The results for the τ−→p¯μ+μ− and τ−→pμ−μ− decay modes represent the first direct experimental limits on these channels.