Maximal compact normal subgroups

The main concern is the existence of a maximal compact normal subgroup K in a locally compact group G, and whether or not G/K is a Lie group. G has a maximal compact subgroup if and only if G/G₀ has. Maximal compact subgroups of totally disconnected groups are open. If the bounded part of G is compactly generated, then G has a maximal compact normal subgroup K and if B(G) is open, then G/K is Lie. Generalized FCgroups, compactly generated type I IN-groups, and Moore groups share the same properties.