Submission date: 7 October 2020

Abstract:

We give a new compactness theorem for any metric ultraproducts of family of metric groups. As an application we characterize simplicity of metric ultraproducts of groups and give a couple of examples of new simple groups which are metric ultraproducts of finite and infinite symmetric groups, linear groups and interval exchange transformations group.

Mathematics Subject Classification: 20E32, 20E45, 03C20, 12L10

Keywords and phrases:

Full text arXiv 2010.03394: pdf, ps.