On conjugacy growth of linear groups

被引：8
|
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.
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页码：261 / 277
页数：17
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