Systolic growth of linear groups

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.

Locations

• Proceedings of the American Mathematical Society - View - PDF
• arXiv (Cornell University) - View - PDF
• DataCite API - View