On conjugacy growth of linear groups

Emmanuel Breuillard; Yves Cornulier; Alexander Lubotzky; Chen Meiri

doi:10.1017/S030500411200059X

On conjugacy growth of linear groups

Emmanuel Breuillard^*
, Yves Cornulier
, Alexander Lubotzky
, Chen Meiri

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	261-277
Number of pages	17
Journal	Mathematical Proceedings of the Cambridge Philosophical Society
Volume	154
Issue number	2
DOIs	https://doi.org/10.1017/S030500411200059X
State	Published - Mar 2013

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title = "On conjugacy growth of linear groups",

abstract = "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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N2 - 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.

AB - 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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On conjugacy growth of linear groups

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