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Linear Approximation of Groups and Ultraproducts of Compact Simple Groups / Lineare Gruppenapproximation und Ultraprodukte kompakter einfacher GruppenStolz, Abel 23 October 2013 (has links) (PDF)
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.
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Linear Approximation of Groups and Ultraproducts of Compact Simple GroupsStolz, Abel 17 October 2013 (has links)
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.
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