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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

(CA) closures of analytic groups


Author: David Zerling
Journal: Proc. Amer. Math. Soc. 82 (1981), 133-138
MSC: Primary 22E05
DOI: https://doi.org/10.1090/S0002-9939-1981-0603616-0
MathSciNet review: 603616
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Abstract: An analytic group $ G$ is called $ (CA)$ if the group of inner automorphisms of $ G$ is closed in the Lie group of all bicontinuous automorphisms of $ G$. We introduce the notion of a $ (CA)$ closure for an analytic group and show that every analytic group possesses a $ (CA)$ closure. The definition of uniqueness for such a $ (CA)$ closure is developed and a sufficient condition for uniqueness is given.

We also develop new sufficient conditions for a closed normal analytic subgroup of a $ (CA)$ analytic group to be $ (CA)$.


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DOI: https://doi.org/10.1090/S0002-9939-1981-0603616-0
Article copyright: © Copyright 1981 American Mathematical Society