Maximal compact normal subgroups and pro-Lie groups
R. W. Bagley and T. S. Wu
Proc. Amer. Math. Soc. 93 (1985), 373-376
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Abstract: We are concerned with conditions under which a locally compact group has a maximal compact normal subgroup and whether or not is a Lie group. If has small compact normal subgroups such that is a Lie group, then is pro-Lie. If in there is a collection of closed normal subgroups such that and is a Lie group for each , then 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.
W. Bagley, T.
S. Wu, and J.
S. Yang, Pro-Lie groups, Trans. Amer. Math. Soc. 287 (1985), no. 2, 829–838. MR 768744
Grosser and Martin
Moskowitz, Compactness conditions in topological groups, J.
Reine Angew. Math. 246 (1971), 1–40. MR 0284541
- R. W. Bagley, T. S. Wu and J. S. Yang, Pro-Lie groups, Trans. Amer. Math. Soc. (to appear). MR 768744 (86e:22006)
- S. Grosser and M. Moskowitz, Compactness conditions in topological groups, J. Reine Angew. Math. 246 (1971), 1-40. MR 0284541 (44:1766)
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