Divisible rigid groups. IV. Definable subgroups

A group $G$ is said to be rigid if it contains a normal series
$$G=G_1>G_2>\ldots>G_m>G_{m+1}=1,$$
whose quotients $G_i/G_{i+1}$ are Abelian and, when treated as right $\mathbb{Z} [G/G_i]$-modules, are torsion-free. A rigid group $G$ is divisible if elements of the quotient $G_i/G_{i+1}$ are divisible by nonzero elements of the ring $\mathbb{Z} [G/G_i]$. We describe subgroups of a divisible rigid group which are definable in the signature of the theory of groups without parameters and with parameters.