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.
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa.de:bsz:15-qucosa-125643 |
| Date | 23 October 2013 |
| Creators | Stolz, Abel |
| Contributors | Universität Leipzig, Fakultät für Mathematik und Informatik, Prod. Dr. Andreas Thom, Prof. Dr. Andreas Thom, Prof. Dr. Nikolay Nikolov |
| Publisher | Universitätsbibliothek Leipzig |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | doc-type:doctoralThesis |
| Format | application/pdf |
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