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Linear Approximation of Groups and Ultraproducts of Compact Simple Groups

We derive basic properties of groups which can be approximated with matrices. These include closure of classes of such groups under group theoretic constructions including direct and inverse limits and free products. We show that metric ultraproducts of projective linear groups over fields of different characteristics are not isomorphic. We further prove that the lattice of normal subgroups in ultraproducts of compact simple groups is distributive. It is linearly ordered in the case of finite simple groups or Lie groups of bounded rank.

Identiferoai:union.ndltd.org:DRESDEN/oai:qucosa:de:qucosa:12191
Date17 October 2013
CreatorsStolz, Abel
ContributorsThom, Andreas, Nikolov, Nikolay, Universität Leipzig
Source SetsHochschulschriftenserver (HSSS) der SLUB Dresden
LanguageEnglish
Detected LanguageEnglish
Typedoc-type:doctoralThesis, info:eu-repo/semantics/doctoralThesis, doc-type:Text
Rightsinfo:eu-repo/semantics/openAccess

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