Compact Subgroups of Lie Groups and Locally Compact Groups

Karl H. Hofmann, Christian Terp
1994 Proceedings of the American Mathematical Society  
We show that the set of compact subgroups in a connected Lie group is inductive. In fact, a locally compact group G has the inductivity property for compact subgroups if and only if the factor group G/Gq modulo the identity component has it.
doi:10.2307/2159906 fatcat:h32fm4juenbebdo5cusfpdi5de