- AutorIn
- Abel Stolz
- Titel
- Linear Approximation of Groups and Ultraproducts of Compact Simple Groups
- Zitierfähige Url:
- https://nbn-resolving.org/urn:nbn:de:bsz:15-qucosa-125643
- Übersetzter Titel (DE)
- Lineare Gruppenapproximation und Ultraprodukte kompakter einfacher Gruppen
- Datum der Einreichung
- 23.04.2013
- Datum der Verteidigung
- 17.10.2013
- Abstract (EN)
- 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.
- Freie Schlagwörter (DE)
- sofische Gruppen, linear sofische Gruppen, Ultraprodukte, metrische Ultraprodukte, kompakte einfache Gruppen
- Freie Schlagwörter (EN)
- sofic groups, linearly sofic groups, ultraproducts, metric ultraproducts, compact simple groups
- Klassifikation (DDC)
- 500
- GutachterIn
- Prod. Dr. Andreas Thom
- Prof. Dr. Nikolay Nikolov
- BetreuerIn
- Prod. Dr. Andreas Thom
- Den akademischen Grad verleihende / prüfende Institution
- Universität Leipzig, Leipzig
- URN Qucosa
- urn:nbn:de:bsz:15-qucosa-125643
- Veröffentlichungsdatum Qucosa
- 23.10.2013
- Dokumenttyp
- Dissertation
- Sprache des Dokumentes
- Englisch