Metric ultraproducts of finite simple groups

2014/02/03 by Thom, Andreas, Wilson, John S.
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1402.0341

Abstract

Some new results on metric ultraproducts of finite simple groups are presented. Suppose that G is such a group, defined in terms of a non-principal ultrafilter ω on N and a sequence (G_i)_{i ∈ N} of finite simple groups, and that G is neither finite nor a Chevalley group over an infinite field. Then G is isomorphic to an ultraproduct of alternating groups or to an ultraproduct of finite simple classical groups. The isomorphism type of G determines which of these two cases arises, and, in the latter case, the ω-limit of the characteristics of the groups Gi. Moreover G is a complete path-connected group with respect to the natural metric on G.

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