GROWTH IN GROUPS: IDEAS AND PERSPECTIVES

被引：29

作者：

Helfgott, Harald A. ^{[1
]}

机构：

[1] Ecole Normale Super, Dept Math, F-75230 Paris, France

来源：

BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY | 2015年 / 52卷 / 03期

关键词：

RANDOM-WALKS; ARITHMETIC PROGRESSIONS; APPROXIMATE GROUPS; PERMUTATION-GROUPS; DIAMETER BOUNDS; EXPANDER GRAPHS; CAYLEY-GRAPHS; SPECTRAL GAP; SUBGROUPS; THEOREM;

D O I：

10.1090/S0273-0979-2015-01475-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This is a survey of methods developed in the last few years to prove results on growth in non-commutative groups. These techniques have their roots in both additive combinatorics and group theory, as well as other fields. We discuss linear algebraic groups, with SL2(Z/pZ) as the basic example, as well as permutation groups. The emphasis will lie on the ideas behind the methods.

引用

页码：357 / 413

页数：57

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