Suitable sets for subgroups of direct sums of discrete groups

Let G=circled plusα<τGα be the direct sum of (discrete) groups endowed with the linear group topology whose base at the identity consists of the subgroups Uα=circled plusαless-than-or-equals, slantβ<τGβ, α<τ. We show that every subgroup H of G has a generating suitable set. In addition, if H is not closed in G, then H has a closed generating suitable set. The case of topologically orderable topological groups is considered. It is proved that if a topologically orderable group G has a (closed) suitable set, then every dense subgroup of G also has a (closed) suitable set.