  We present easily verifiable sufficient conditions of time-independence and
commutativity for local and nonlocal symmetries for a large class of
homogeneous (1+1)-dimensional evolution systems. In contrast with the majority
of known results, the verification of our conditions does not require the
existence of master symmetry or hereditary recursion operator for the system in
question. We also give simple sufficient conditions for the existence of
infinite sets of time-independent symmetries for homogeneous (1+1)-dimensional
evolution systems within slightly modified master symmetry approach.
