Symmetry properties of renormalized theories with symmetrical classical action

The paper deals with the proof of the field theory symmetry conservation after the renormalization. Properties of the renormalized action symmetry Ssub(R) and the generating functional of vertex functions GITAsub(R) are studied under the condition that a classical action S0 possesses some symmetry. It is shown that in this case the Ssub(R) action and the GITAsub(R) functional also possess some symmetry. The theories are first considered without gauge symmetries, and then the same problem is considered in gauge theories of a general type