Submission date: 30 July 2019

Abstract:

Tent and Ziegler proved that the automorphism group of the Urysohn sphere is simple and that the automorphism group of the Urysohn space is simple modulo bounded automorphisms. In this paper we extend their methods and prove simplicity for many homogeneous structures which admit a metric-like amalgamation, in particular, we get simplicity of the automorphism groups of all primitive 3-constrained metrically homogeneous graphs of finite diameter from Cherlin's list. This generalisation is motivated by results of Hubička, Konečný and Nešetřil on semigroup-valued metric spaces.

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Full text arXiv 1907.13204: pdf, ps.