Properties of symmetry of renormalized theories with a symmetric classical action

Symmetry properties of renormalized action Ssub(R) and generating functional of vertex functions Gsub(R) under condition, that classical action S0 possesses a certain symmetry, are investigated. It is shown, that in this case Ssub(R) and Gsub(R) also possess a certain symmetry. Theories without gauge symmetries and gauge theories of general type are studied. It is shown, that symmetries of the initial classical action correspond to the symmetry of modified and effective actions