Divisible Rigid Groups. IV. Definable Subgroups

A group G is said to be rigid if it contains a normal series G = G1 > G2 > … > Gm > Gm+1 = 1, whose quotients Gi/Gi+1 are Abelian and, when treated as right ℤ[G/Gi]-modules, are torsion-free. A rigid group G is divisible if elements of the quotient Gi/Gi+1 are divisible by nonzero elements of the ring ℤ[G/Gi]. We describe subgroups of a divisible rigid group which are definable in the signature of the theory of groups without parameters and with parameters.