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Existing permutation-invariant methods can be divided into two categories according to the aggregation scope, i.e. global aggregation and local one. Although the global aggregation methods, e. g., PointNet and Deep Sets, get involved in simpler structures, their performance is poorer than the local aggregation ones like PointNet++ and Point Transformer. It remains an open problem whether there exists a global aggregation method with a simple structure, competitive performance, and even much fewer parameters. In this paper, we propose a novel global aggregation permutation-invariant network based on dual MLP dot-product, called DuMLP-Pin, which is capable of being employed to extract features for set inputs, including unordered or unstructured pixel, attribute, and point cloud data sets. We strictly prove that any permutation-invariant function implemented by DuMLP-Pin can be decomposed into two or more permutation-equivariant ones in a dot-product way as the cardinality of the given input set is greater than a threshold. We also show that the DuMLP-Pin can be viewed as Deep Sets with strong constraints under certain conditions. The performance of DuMLP-Pin is evaluated on several different tasks with diverse data sets. The experimental results demonstrate that our DuMLP-Pin achieves the best results on the two classification problems for pixel sets and attribute sets. On both the point cloud classification and the part segmentation, the accuracy of DuMLP-Pin is very close to the so-far best-performing local aggregation method with only a 1-2% difference, while the number of required parameters is significantly reduced by more than 85% in classification and 69% in segmentation, respectively. The code is publicly available on https://github.com/JaronTHU/DuMLP-Pin.