Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Maximal compact normal subgroups and pro-Lie groups

Authors: R. W. Bagley and T. S. Wu
Journal: Proc. Amer. Math. Soc. 93 (1985), 373-376
MSC: Primary 22D05
MathSciNet review: 770558
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 22D05

Retrieve articles in all journals with MSC: 22D05

Additional Information

Article copyright: © Copyright 1985 American Mathematical Society

American Mathematical Society