On small sumsets in \((\mathbb{Z}/2\mathbb{Z})^n\)
For a subset \(\mathcal A\) of \((\mathbb Z/2\mathbb Z)^n\) for which \(| 2\mathcal A| \leq c| \mathcal A| \) obtains for some constant \(c<4\) it is shown that \(\mathcal A\) is contained in the coset of a subgroup of \((\mathbb Z/2\mathbb Z)^n\) which has order bounded by \(u(c)\). The function \(u(c)\) for small \(c\) is given by \(u(c)={-c^3+3c-1\over 2c-1}\). This yields structural results on such sets \(\mathcal A\) improving earlier results of \textit{I. Z. Ruzsa} [''Structure theory of set addition'', Asterisque, Deshouillers, Landreau, Yudin eds; 258, 323-326 (1999; Zbl 0946.11007)].
scientific article; zbMATH DE number 2108688