Decisive subgroups of analytic groups
Author:
T. Christine Stevens
Journal:
Trans. Amer. Math. Soc. 274 (1982), 101-108
MSC:
Primary 22E15; Secondary 54A10
DOI:
https://doi.org/10.1090/S0002-9947-1982-0670922-9
MathSciNet review:
670922
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Abstract | References | Similar Articles | Additional Information
Abstract: It is known that every analytic group contains a closed abelian subgroup
which is "decisive" in the sense that the Hausdorff topologies for
which are weaker than
are completely determined by their restrictions to
. We show here that
must ordinarily contain the entire center of
but that the rest of
can in general be reduced. The proof involves constructing "unusual" topologies for abelian Lie groups.
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9947-1982-0670922-9
Keywords:
Analytic group,
Lie group,
(CA) analytic group
Article copyright:
© Copyright 1982
American Mathematical Society