Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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)$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 22E15

Retrieve articles in all journals with MSC: 22E15


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1975-0364548-0
PII: S 0002-9947(1975)0364548-0
Article copyright: © Copyright 1975 American Mathematical Society