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On conjugacy growth of linear groups†

Published online by Cambridge University Press:  31 October 2012

EMMANUEL BREUILLARD ,
YVES CORNULIER ,
ALEXANDER LUBOTZKY  and
CHEN MEIRI
EMMANUEL BREUILLARD
Affiliation:
Laboratoire de Mathématiques, Bâtiment 425, Université Paris-Sud 11, 91405 Orsay, France. e-mail: emmanuel.breuillard@math.u-psud.fr, yves.cornulier@math.u-psud.fr
YVES CORNULIER
Affiliation:
Laboratoire de Mathématiques, Bâtiment 425, Université Paris-Sud 11, 91405 Orsay, France. e-mail: emmanuel.breuillard@math.u-psud.fr, yves.cornulier@math.u-psud.fr
ALEXANDER LUBOTZKY
Affiliation:
Einstein institute of Mathematics, Hebrew University, Jerusalem 91904, Israel. e-mail: alexlub@math.huji.ac.il, chen.meiri@mail.huji.ac.il
CHEN MEIRI
Affiliation:
Einstein institute of Mathematics, Hebrew University, Jerusalem 91904, Israel. e-mail: alexlub@math.huji.ac.il, chen.meiri@mail.huji.ac.il
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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 GLd 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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 154 , Issue 2 , March 2013 , pp. 261 - 277
Copyright
Copyright © Cambridge Philosophical Society 2012

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Footnotes

†

The authors are grateful for grants from the ERC and the NSF.

References

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