Some geometric properties of metric ultraproducts of finite simple groups

2016/06/13 by Thom, Andreas, Wilson, John · 1 citation
#FOS: Mathematics #Group Theory (math.GR) #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1606.03863

Abstract

In this article we prove some previously announced results about metric ultraproducts of finite simple groups. We show that any non-discrete metric ultraproduct of alternating or special linear groups is a geodesic metric space. For more general non-discrete metric ultraproducts of finite simple groups, we are able to establish path-connectedness. As expected, these global properties reflect asymptotic properties of various families of finite simple groups.

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• Geometric properties of unit groups of von Neumann's continuous rings

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