I assume all tolpological groups here to be Hausdorff. A group is called locally finite if every finitely generated subgroup is finite. What can be said about a locally finite compact group? Must it be finite? Is there any structure theorem for this kind of groups?
For the larger class of torsion compact groups structure theorems exist. In particular, They tell us that these groups are profinite. So, locally finite compact groups are profinite as well. But, can one prove more?