  It is shown that every separable abelian topological group is isomorphic with
a topological subgroup of a monothetic group (that is, a topological group with
a single topological generator). In particular, every separable metrizable
abelian group embeds into a metrizable monothetic group. More generally, we
describe all topological groups that can be embedded into monothetic groups:
they are exactly abelian topological groups of weight $\leq\frak c$ covered by
countably many translations of every nonempty open subset.
