An analog of Freiman's theorem in groups

  title={An analog of Freiman's theorem in groups},
  author={Imre Z. Ruzsa},
It is proved that any set A in a commutative group G where the order of elements is bounded by an integer r having n elements and at most n sums is contained in a subgroup of size An with A = f(r; ) depending on r and but not on n. This is an analog of a theorem of G. Freiman which describes the structure of such sets in the group of integers. Let A be a set of integers, jAj = n, and suppose that jA+Aj cn. A famous theorem of Freiman [1, 2] provides a certain structural description of these… CONTINUE READING
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