Generic Types and Generic Elements in Divisible Rigid Groups

A group G is said to be m-rigid if it contains a normal series of the form G = G ₁ > G ₂ >.. > G_m > G_m+1 = 1, whose quotients G_i/G_i+1 are Abelian and, treated as (right) ℤ[G/G_i]-modules, are torsion-free. A rigid group G is said to be divisible if elements of the quotient ρ_i(G)/ρ_i+1(G) are divisible by nonzero elements of the ring ℤ[G/ρ_i(G)]. Previously, it was proved that the theory of divisible m-rigid groups is complete and ω-stable. In the present paper, we give an algebraic description of elements and types that are generic over a divisible m-rigid group G.