An analog of Freiman's theorem in groups

By Imre Z. Ruzsa. Astérisque, 2018

127 citations recorded by the source corpus.

— It is proved that in a commutative group G, where the order of elements is bounded by an integer r, any set A having n elements and at most cm sums is contained in a subgroup of size Cn with C — /(r, a) depending on r and a 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.

Subfields: Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/51e855a5fef110f0f5ca7ba306b08b512621f3e3

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In Mathematical Physics

Citations in the corpus

Approximate lattices (2016, background): “In this influential paper, the beginnings of the basic theory of such objects, based on previous fundamental works by Freiman [22], Ruzsa [41] and Plünnecke [37], were outlined.”
COMPRESSIONS, CONVEX GEOMETRY AND THE FREIMAN–BILU THEOREM (2005, background): “Ruzsa [19] attributes the analog of this idea in the finite field setting to Katalin Marton.”
The primes contain arbitrarily long polynomial progressions (2006, methodology): “To see this, we use a covering argument of Ruzsa [27].”
On a conjecture of Marton (2023, background): “In this paper we prove a conjecture of Katalin Marton (see [28]), widely known in the literature as the polynomial Freiman–Ruzsa conjecture in characteristic 2.”
Montréal notes on quadratic Fourier analysis (2007, background): “The original reference for Proposition 1.14 is the paper [28] by Imre Ruzsa.”