Systolic growth of linear groups
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- by Khalid Bou-Rabee and Yves Cornulier PDF
- Proc. Amer. Math. Soc. 144 (2016), 529-533 Request permission
Abstract:
We prove that the residual girth of any finitely generated linear group is at most exponential. This means that the smallest finite quotient in which the $n$-ball injects has at most exponential size. If the group is also not virtually nilpotent, it follows that the residual girth and the systolic growth are precisely exponential.References
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Additional Information
- Khalid Bou-Rabee
- Affiliation: The City College of New York, 160 Convent Ave, New York, New York 10031
- MR Author ID: 888620
- Email: khalid.math@gmail.com
- Yves Cornulier
- Affiliation: CNRS – Département de Mathématiques, Université Paris-Sud, 91405 Orsay, France
- MR Author ID: 766953
- Email: yves.cornulier@math.u-psud.fr
- Received by editor(s): August 28, 2014
- Received by editor(s) in revised form: February 3, 2015
- Published electronically: June 30, 2015
- Additional Notes: The first-named author was supported in part by NSF DMS-1405609
The second-named author was supported in part by ANR GSG 12-BS01-0003-01 - Communicated by: Kevin Whyte
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 529-533
- MSC (2010): Primary 20E26; Secondary 11C08, 13B25, 20F65
- DOI: https://doi.org/10.1090/proc12747
- MathSciNet review: 3430831