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arXiv · 2410.23035

Residually finite groups with uniformly almost flat quotients

David Guo·Matthew Tointon
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Abstract

We show that if all the finite coset spaces of a polycyclic group have diameter bounded uniformly below by a polynomial in their size then the group is virtually nilpotent. We obtain the same conclusion for a finitely generated residually torsion-free nilpotent group under the weaker assumption that the finite quotient groups have diameter bounded uniformly below by a polynomial in their size. This extends work of Khukhro and Valette.

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David Guo, Matthew Tointon. 2024-10-30. Residually finite groups with uniformly almost flat quotients. https://arxiv.org/abs/2410.23035

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