On Small Sumsets in (ℤ/2ℤ)n

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.

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Correspondence to Jean-Marc Deshouillers.

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Deshouillers, JM., Hennecart, F. & Plagne, A. On Small Sumsets in (ℤ/2ℤ)n . Combinatorica 24, 53–68 (2004). https://doi.org/10.1007/s00493-004-0004-0

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Mathematics Subject Classification (2000):

  • 11P70
  • 11B75