On conjugacy growth of linear groups

被引：9

作者：

Breuillard, Emmanuel ^{[1
]}

Cornulier, Yves ^{[1
]}

Lubotzky, Alexander ^{[2
]}

Meiri, Chen ^{[2
]}

机构：

[1] Univ Paris 11, Math Lab, F-91405 Orsay, France

[2] Hebrew Univ Jerusalem, Einstein Inst Math, IL-91904 Jerusalem, Israel

来源：

MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY | 2013年 / 154卷 / 02期

基金：

欧洲研究理事会; 美国国家科学基金会;

关键词：

UNIFORM EXPONENTIAL-GROWTH; ZARISKI-DENSE SUBGROUPS; STRONG APPROXIMATION;

D O I：

10.1017/S030500411200059X

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We investigate the conjugacy growth of finitely generated linear groups. We show that finitely generated non-virtually-solvable subgroups of GL(d) have uniform exponential conjugacy growth and in fact that the number of distinct polynomials arising as characteristic polynomials of the elements of the ball of radius n for the word metric has exponential growth rate bounded away from 0 in terms of the dimension d only.

引用

页码：261 / 277

页数：17

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