, Volume 24, Issue 1, pp 53-68

On Small Sumsets in (ℤ/2ℤ) n

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It is proved that any subset $ {\user1{A}} $ of (ℤ/2ℤ) n , having k elements, such that $ {\left| {{\user1{A}} + {\user1{A}}} \right|} = c{\left| {\user1{A}} \right|} $ (with c<4), is contained in a subgroup of order at most u −1k where u=u(c)>0 is an explicit function of c which does not depend on k nor on n. This improves by a radically different method the corresponding bounds deduced from a more general result of I. Z. Ruzsa.