In this note, we prove that in a Hausdorff topological abelian group, the closed subgroup generated by all compact elements is equal to teh closed subgroup generated by all compact elements which are topologically p-torsion for some prime p. In particular, this yields a new, short solution to a question raised by Armacost [A]. Using Pontrjagin duality, we obtain new descriptions of the identity component of a locally compact abelian group.
Loth, P. (2005). Compact topologically torsion elements of topological abelian groups. Rendiconti del Seminario Matematico della Università di Padova, 113, 117-123. .