Submission date: 3 February 2014.

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 \in 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 G_i. Moreover G is a complete path-connected group with respect to the natural metric on G.

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Full text arXiv 1402.0341: pdf, ps.