Geometric Group Theory Seminar
Title: Residually finite groups with uniformly almost flat quotients.
Speaker: David Guo
University: University of Bristol
Abstract:
Given a residually finite group, there is considerable interest in understanding what information is encoded in the finite quotients. Khukhro and Valette in- vestigated what algebraic properties we can deduce from the diameter of finite quotients of the group. They showed that the finite quotients have diameter bounded uniformly below by a constant multiple of their size if and only if the group is virtually cyclic, and that if the diameter of finite quotients is bounded uniformly below by a polynomial in their size then the group virtually maps onto Z. We built on their work by showing that the later assumption in fact implies being virtually nilpotent in various specific classes of groups. We take this opportunity to propose future research to characterise finitely generated residually finite groups that satisfy this condition. Joint work with Matthew Tointon.
