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arXiv · 1606.03863

Some geometric properties of metric ultraproducts of finite simple groups

Andreas Thom·John Wilson
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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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Andreas Thom, John Wilson. 2016-06-13. Some geometric properties of metric ultraproducts of finite simple groups. https://arxiv.org/abs/1606.03863

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