 ZERODIMENSIONAL SYMMETRY SEMINAR
 Speaker: Dr Alejandra Garrido, The University of Newcastle
 Title: Hausdorff dimension and normal subgroups of freelike prop groups
 Location: Room LG 17, McMullin (Callaghan Campus) The University of Newcastle
 Time and Date: 2:00 pm, Tue, 27^{th} Nov 2018
 Abstract:
Hausdorff dimension has become a standard tool to measure the "size" of fractals in real space. However, it can be defined on any metric space and therefore can be used to measure the "size" of subgroups of, say, prop groups (with respect to a chosen metric). This line of investigation was started 20 years ago by Barnea and Shalev, who showed that padic analytic groups do not have any "fractal" subgroups, and asked whether this characterises them among finitely generated prop groups.
I will explain what all of this means and report on joint work with Oihana Garaialde and Benjamin Klopsch in which, while trying to solve this problem, we ended up showing an analogue of a theorem of Schreier in the context of prop groups of positive rank gradient: any finitely generated infinite normal subgroup of a prop group of positive rank gradient is of finite index. I will also explain what "positive rank gradient" means, and why prop groups with such a property are "freelike".
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