Maximal compact normal subgroups and pro-Lie groups
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- by R. W. Bagley and T. S. Wu PDF
- Proc. Amer. Math. Soc. 93 (1985), 373-376 Request permission
Abstract:
We are concerned with conditions under which a locally compact group $G$ has a maximal compact normal subgroup $K$ and whether or not $G/K$ is a Lie group. If $G$ has small compact normal subgroups $K$ such that $G/K$ is a Lie group, then $G$ is pro-Lie. If in $G$ there is a collection of closed normal subgroups $\{ {H_\alpha }\}$ such that $\cap {H_\alpha } = e$ and $G/{H_\alpha }$ is a Lie group for each $\alpha$, then $G$ is a residual Lie group. We determine conditions under which a residual Lie group is pro-Lie and give an example of a residual Lie group which is not embeddable in a pro-Lie group.References
- R. W. Bagley, T. S. Wu, and J. S. Yang, Pro-Lie groups, Trans. Amer. Math. Soc. 287 (1985), no. 2, 829–838. MR 768744, DOI 10.1090/S0002-9947-1985-0768744-6
- Siegfried Grosser and Martin Moskowitz, Compactness conditions in topological groups, J. Reine Angew. Math. 246 (1971), 1–40. MR 284541, DOI 10.1515/crll.1971.246.1
Additional Information
- © Copyright 1985 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 93 (1985), 373-376
- MSC: Primary 22D05
- DOI: https://doi.org/10.1090/S0002-9939-1985-0770558-3
- MathSciNet review: 770558