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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Normal subgroups of $ {\rm Diff}\sp{\Omega }({\bf R}\sp{3})$


Author: Francisca Mascaró
Journal: Proc. Amer. Math. Soc. 92 (1984), 609-614
MSC: Primary 58D05; Secondary 57R50
MathSciNet review: 760953
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Abstract: Let $ \Omega $ be a volume element on $ {{\mathbf{R}}^3}$ of infinite total $ \Omega $-volume. We denote by $ {\operatorname{Dif}}{{\text{f}}^\Omega }({{\mathbf{R}}^3})$ the group of all $ \Omega $-preserving diffeomorphisms of $ {{\mathbf{R}}^3}$, by $ {\operatorname{Diff}}_{\text{c}}^\Omega ({{\mathbf{R}}^3})$ the subgroup of all elements with compact support and by $ {\operatorname{Diff}}_{\text{f}}^{\Omega}(\mathbf{R}^3)$ the subgroup of all elements whose support has finite $ \Omega $-volume.

We prove that there is no normal subgroup between $ {\operatorname{Diff}}_{\text{c}}^\Omega ({{\mathbf{R}}^3})$ and $ {\operatorname{Diff}}_{\text{f}}^\Omega ({{\mathbf{R}}^3})$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1984-0760953-X
PII: S 0002-9939(1984)0760953-X
Article copyright: © Copyright 1984 American Mathematical Society