Aims. The theoretical model for magnetohydrodynamic (MHD) modes guided by a field-aligned plasma cylinder with a steady flow is adapted to interpret transverse waves observed in solar coronal hot jets, discovered with Hinode/XRT in terms of fast magnetoacoustic kink modes.\ud Methods. Dispersion relations for linear magnetoacoustic perturbations of a plasma jet of constant cross-section surrounded by static magnetised plasma are used to determine the phase and group speeds of guided transverse waves and their relationship with the physical parameters of the jet and the background plasma. The structure of the perturbations in the macroscopic parameters of the plasma inside and outside the jet, and the phase relations between them are also established.\ud Results. We obtained a convenient expansion for the long wave-length limit of the phase and group speeds and have shown that transverse waves observed in soft-X-ray solar coronal jets are adequately described in terms of fast magnetoacoustic kink modes by a magnetic cylinder model, which includes the effect of a steady flow. In the observationally determined range of parameters, the waves\ud are not found to be subject to either the Kelvin-Helmholtz instability or the negative energy wave instability, and hence they are likely to be excited at the source of the jet
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