Systolic growth of linear groups

Bou-Rabee, Khalid; Cornulier, Yves

doi:10.1090/proc12747

Systolic growth of linear groups
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by Khalid Bou-Rabee and Yves Cornulier

Proc. Amer. Math. Soc. 144 (2016), 529-533

DOI: https://doi.org/10.1090/proc12747

Published electronically: June 30, 2015

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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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