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Some geometric properties of metric ultraproducts of finite simple groups. (English) Zbl 1469.20015

Summary: In this article we prove some previously announced results about metric ultraproducts of finite simple groups [C. R., Math., Acad. Sci. Paris 352, No. 6, 463–466 (2014; Zbl 1323.22003)]. 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.

MSC:

20D06 Simple groups: alternating groups and groups of Lie type
22E40 Discrete subgroups of Lie groups

Citations:

Zbl 1323.22003
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References:

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