Topological locally \=F\=C-groups (Q791679)

In this paper some theorems about the class LFC of topological groups (i.e. any finitely generated compact subgroup is in \(\overline{FC}\) class) are obtained. This class contains topological locally finite groups and - of course - \(\overline{FC}\)-groups. In particular the following theorems are proved: 1. A locally compact compactly generated LFC-group is an \(\overline{FC}\)-group (Theorem 3). 2. If the factor group G/(centre) is locally finite, then G is an LFC-group.