Proc. London Math. Soc.
Abstract of Paper PLMS 1370
A precise description of a subset $\mathcal{A}$ of $\mathbb{Z} / n \mathbb{Z}$ satisfying
$$ | \mathcal{A} + \mathcal{A} | \leq 2.04 | \mathcal{A} | $$
is given. Basically, there exists a subgroup $\mathcal{H}$ of $\mathbb{Z} / n \mathbb{Z}$ such that $\mathcal{A}$ is included in an arithmetic progression of $\ell$ cosets modulo $\mathcal{H}$ and
$$(\ell - 1) | \mathcal{H} | \leq | \mathcal{A} + \mathcal{A} | - | \mathcal{A} |.$$
2000 Mathematical Subject Classification: 11B50, 11B83, 20E34.
Keywords: additive number theory, Kneser's theorem, structure theory of set addition, finite abelian groups.
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