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arXiv · 1106.4773

On conjugacy growth of linear groups

Emmanuel Breuillard·Yves de Cornulier·Alexander Lubotzky·Chen Meiri
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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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Emmanuel Breuillard, Yves de Cornulier, Alexander Lubotzky, Chen Meiri. 2011-06-23. On conjugacy growth of linear groups. https://doi.org/10.1017/s030500411200059x

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