Sets with small sumset and rectification

BJ Green; IZ Ruzsa

doi:10.1112/S0024609305018102

Sets with small sumset and rectification

BJ Green
, IZ Ruzsa

School of Mathematics

Research output: Contribution to journal › Article (Academic Journal) › peer-review

51 Citations (Scopus)

Abstract

We study the extent to which sets A subset of Z/NZ, AF prime, resemble sets of integers from the additive point of view ('up to Freiman isomorphism'). We give a direct proof of a result of Freiman, namely that if vertical bar A + A vertical bar = (32K)(-12K2). As a byproduct of our argument we obtain a sharpening of the second author's result on sets with small sumset in torsion groups. For example, if A subset of F-2(n), and if vertical bar A + A vertical bar

Translated title of the contribution	Sets with small sumset and rectification
Original language	English
Pages (from-to)	43 - 52
Number of pages	10
Journal	Bulletin of the London Mathematical Society
Volume	38 (1)
DOIs	https://doi.org/10.1112/S0024609305018102
Publication status	Published - Feb 2006

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Publisher: Oxford University Press
Other identifier: IDS Number: 012QT

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http://blms.oxfordjournals.org/cgi/content/abstract/38/1/43

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title = "Sets with small sumset and rectification",

abstract = "We study the extent to which sets A subset of Z/NZ, AF prime, resemble sets of integers from the additive point of view ('up to Freiman isomorphism'). We give a direct proof of a result of Freiman, namely that if vertical bar A + A vertical bar = (32K)(-12K2). As a byproduct of our argument we obtain a sharpening of the second author's result on sets with small sumset in torsion groups. For example, if A subset of F-2(n), and if vertical bar A + A vertical bar ",

author = "BJ Green and IZ Ruzsa",

note = "Publisher: Oxford University Press Other identifier: IDS Number: 012QT ",

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language = "English",

volume = "38 (1)",

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journal = "Bulletin of the London Mathematical Society",

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AU - Green, BJ

AU - Ruzsa, IZ

N1 - Publisher: Oxford University Press Other identifier: IDS Number: 012QT

PY - 2006/2

Y1 - 2006/2

N2 - We study the extent to which sets A subset of Z/NZ, AF prime, resemble sets of integers from the additive point of view ('up to Freiman isomorphism'). We give a direct proof of a result of Freiman, namely that if vertical bar A + A vertical bar = (32K)(-12K2). As a byproduct of our argument we obtain a sharpening of the second author's result on sets with small sumset in torsion groups. For example, if A subset of F-2(n), and if vertical bar A + A vertical bar

AB - We study the extent to which sets A subset of Z/NZ, AF prime, resemble sets of integers from the additive point of view ('up to Freiman isomorphism'). We give a direct proof of a result of Freiman, namely that if vertical bar A + A vertical bar = (32K)(-12K2). As a byproduct of our argument we obtain a sharpening of the second author's result on sets with small sumset in torsion groups. For example, if A subset of F-2(n), and if vertical bar A + A vertical bar

U2 - 10.1112/S0024609305018102

DO - 10.1112/S0024609305018102

M3 - Article (Academic Journal)

SN - 1469-2120

VL - 38 (1)

SP - 43

EP - 52

JO - Bulletin of the London Mathematical Society

JF - Bulletin of the London Mathematical Society

ER -

Sets with small sumset and rectification

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