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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Dense subgroups of Lie groups. II


Author: David Zerling
Journal: Trans. Amer. Math. Soc. 246 (1978), 419-428
MSC: Primary 22E15
MathSciNet review: 515548
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Abstract: Let G be a dense analytic subgroup of an analytic group L. Then G contains a maximal (CA) closed normal analytic suhgroup M and a closed abelian subgroup $ A = Z(G) \times E$, where E is a closed vector subgroup of G, such that $ G = M \cdot A$, $ M \cap A = Z(G)$, $ \overline M = M \cdot \overline {Z(G)} $, and $ L = M \cdot \overline A $.

We also indicate the extent to which a (CA) analytic group is uniquely determined by its center and a dense analytic subgroup.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1978-0515548-1
PII: S 0002-9947(1978)0515548-1
Keywords: (CA) Lie group, (CA) Lie algebra, automorphism group, semidirect product, dense subgroup, dense subalgebra
Article copyright: © Copyright 1978 American Mathematical Society