On a theorem of Deshouillers and Freiman

The “structure theory of set addition” has been well studied in the last fifty years, after the works of Freiman. In [1] Deshouillers and Freiman established a structure theorem for subsets of Z∕nZ with small doubling constant. In this article we provide a simpler proof of the structure theorem of [1], and on our way we also obtain some improvements.