We investigate the question of whether or not the orbit of a point in A/Q, under the natural action of a subset Σ⊆Q, is dense in A/Q. We prove that if the set Σ is a multiplicative semigroup of Q^× which contains at least two multiplicatively independent elements, one of which is an integer, then the orbit Σα of any point α with irrational real coordinate is dense.

Research of both authors supported by EPSRC grant EP/J00149X/1.