Decisive subgroups of analytic groups

Stevens, T. Christine

doi:10.1090/S0002-9947-1982-0670922-9

Decisive subgroups of analytic groups
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by T. Christine Stevens

Trans. Amer. Math. Soc. 274 (1982), 101-108

DOI: https://doi.org/10.1090/S0002-9947-1982-0670922-9

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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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