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The Ising or Ports models of ferromagnetism have been widely used to describe locally interacting social or economic systems. We consider a related model, introduced by Sznajd to describe the evolution of consensus in the scale-free networks with the tunable strength (noted by Q) of community structure. In the Sznajd model, the opinion or state of any spins can only be changed by the influence of neighbouring pairs of similar connection spins.Such pairs can polarize their neighbours. Using asynchronous updating, it is found that the smaller the community strength Q, the larger the slope of the exponential relaxation time distribution. Then the effect of the initial upspin concentration p as a function of the final all up probability E is investigated by taking different initialization strategies, the random node-chosen initialization strategy has no difference under different community strengths,while the strategies of community node-chosen initialization and hub node-chosen initialization are different in final probability under different Q, and the latter one is more effective in reaching final state.