It is a challenge to understand why cooperation is prevalent in human society, especially without a mechanism that benefits cooperators such as direct, indirect and strong reciprocity. We study an evolutionary process of public goods game among individuals in multiple groups in a population. We find that the existence of an independent cooperator group is beneficial to the rise of cooperation in the population, which is applicable to both Moran process and a so-called disaster update process proposed in this paper. However, the introduction of ...