Time dependence and (non)commutativity of symmetries of evolution equations

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.