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Proceedings of the American Mathematical Society

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

 

 

On the nonexistence of slices for $ p$-adic transformation groups


Author: Lawrence M. Franklin
Journal: Proc. Amer. Math. Soc. 27 (1971), 183-185
MSC: Primary 22.40
DOI: https://doi.org/10.1090/S0002-9939-1971-0267039-2
MathSciNet review: 0267039
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Abstract: If a compact Lie group acts effectively on a manifold, then local cross-sections to the orbit structure can be constructed. They are called slices. We prove that if a compact group acts effectively on a manifold, but it is not a Lie group, then a slice cannot exist at every point.


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DOI: https://doi.org/10.1090/S0002-9939-1971-0267039-2
Keywords: Hilbert-Smith conjecture, slice, transformation group, $ p$-adic group
Article copyright: © Copyright 1971 American Mathematical Society