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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Some theorems on $ ({\rm CA})$ analytic groups

Author: David Zerling
Journal: Trans. Amer. Math. Soc. 205 (1975), 181-192
MSC: Primary 22E15
MathSciNet review: 0364548
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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$. We show that each non-$ (CA)$ analytic group $ G$ can be written as a semidirect product of a $ (CA)$ analytic group and a vector group. This decomposition yields a natural dense immersion of $ G$ into a $ (CA)$ analytic group $ H$, such that each automorphism of $ G$ can be extended to an automorphism of $ H$. This immersion and extension property enables us to derive a sufficient condition for the normal part of a semidirect product decomposition of a $ (CA)$ analytic group to be $ (CA)$.

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Article copyright: © Copyright 1975 American Mathematical Society