A topological group G is said an AFG -group if G contains an increasing sequence of finite subgroups having dense union.In this paper it is proved that the identity component G 0 of a locally compact AFG -group G is a pro-torus.This partially answers an old open question posed by Ross and Stromberg in Pacific J. Math., 20 (1967), 135-147.Other results included in this paper give a necessary and sufficient condition for an almost connected Lie group to be an AFG-group.
H. Hamrouni (Thu,) studied this question.