New proofs of Plunnecke-type estimates for product sets in groups

被引：54

作者：

Petridis, Giorgis ^{[1
]}

机构：

[1] Univ Rochester, Dept Math, Rochester, NY 14617 USA

来源：

COMBINATORICA | 2012年 / 32卷 / 06期

关键词：

11P70;

D O I：

10.1007/s00493-012-2818-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We present a new method to bound the cardinality of product sets in groups and give three applications. A new and unexpectedly short proof of the Plunnecke-Ruzsa sumset inequalities for commutative groups. A new proof of a theorem of Tao on triple products, which generalises these inequalities when no assumption on commutativity is made. A further generalisation of the Plunnecke-Ruzsa inequalities in general groups.

引用

页码：721 / 733

页数：13

共 16 条

[1]

[Anonymous], COMBINATORIAL NUMBER

[2]

[Anonymous], 1976, Combinatorics: Colloq. Math. Soc. Janos Bolyai

[3]

Granville A, 2007, CRM PROC & LECT NOTE, V43, P1

[4] Growth and generation in SL2(Z/pZ) [J].

Helfgott, H. A. .

ANNALS OF MATHEMATICS, 2008, 167 (02) :601-623

[5] ON A THEOREM OF PLUNNECKE CONCERNING THE SUM OF A BASIS AND A SET OF POSITIVE DENSITY [J].

MALOUF, JL .

JOURNAL OF NUMBER THEORY, 1995, 54 (01) :12-22

[6]

PLUNNECKE H, 1970, J REINE ANGEW MATH, V243, P171

[7]

Ruzsa I.Z., 2010, BOLYAI SOC MATH STUD, V21, P591, DOI DOI 10.1007/978-3-642-14444-8

[8]

Ruzsa I. Z., 1989, SCI A, V3, P97

[9]

Ruzsa I. Z., 1990, SCIENTIA A, V4, P93

[10]

Ruzsa IZ, 1999, ASTERISQUE, P323

← 1 2 →