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We have carried out numerical simulations of the convection zone in a K dwarf of 0.7 solar masses rotating at the solar rotation period. We study the convection pattern, the differential rotation and meridional flows, and the dynamo-generated magnetic field. We find that for a star of this type, the solar rotation period represents a case of fairly rapid rotation and the differential is solar-type. A dynamo-generated large scale field appears but it is neither dipolar nor does it show a simple activity cycle.