$(\textrm {CA})$ topological groups
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- by David Zerling PDF
- Proc. Amer. Math. Soc. 54 (1976), 345-351 Request permission
Abstract:
A locally compact topological group $G$ is called $(CA)$ if the group of inner automorphisms of $G$ is closed in the group of all bicontinuous automorphisms of $G$. We show that each non-$(CA)$ locally compact connected group $G$ can be written as a semidirect product of a $(C A)$ locally compact connected group by a vector group. This decomposition yields a natural dense imbedding of $G$ into a $(C A)$ locally compact connected group $P$, such that each bicontinuous automorphism of $G$ can be extended to a bicontinuous automorphism of $P$. This imbedding and extension property enables us to derive a sufficient condition for the normal part of a semidirect product decomposition of a $(C A)$ locally compact connected group to be $(C A)$.References
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Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 54 (1976), 345-351
- MSC: Primary 22D05
- DOI: https://doi.org/10.1090/S0002-9939-1976-0412337-7
- MathSciNet review: 0412337