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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Decisive subgroups of analytic groups


Author: T. Christine Stevens
Journal: Trans. Amer. Math. Soc. 274 (1982), 101-108
MSC: Primary 22E15; Secondary 54A10
MathSciNet review: 670922
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Abstract: It is known that every analytic group $ (L,\tau )$ contains a closed abelian subgroup $ H$ which is "decisive" in the sense that the Hausdorff topologies for $ L$ which are weaker than $ \tau $ are completely determined by their restrictions to $ H$. We show here that $ H$ must ordinarily contain the entire center of $ L$ but that the rest of $ H$ can in general be reduced. The proof involves constructing "unusual" topologies for abelian Lie groups.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1982-0670922-9
PII: S 0002-9947(1982)0670922-9
Keywords: Analytic group, Lie group, (CA) analytic group
Article copyright: © Copyright 1982 American Mathematical Society