Abstract
A group G is said to be rigid if it contains a normal series G = G1 > G2 > . . . > G m > Gm+1 = 1, whose quotients G i /Gi+1 are Abelian and, treated as right ℤ[G/G i ]- modules, are torsion-free. A rigid group G is divisible if elements of the quotient G i /Gi+1 are divisible by nonzero elements of the ring ℤ[G/G i ]. Every rigid group is embedded in a divisible one. Previously, it was stated that the theory 𝔗 m of divisible m-rigid groups is complete. Here, it is proved that this theory is ω-stable. Furthermore, we describe saturated models, study elementary submodels of an arbitrary model, and find a representation for a countable saturated model in the form of a limit group in the Fraisse system of all finitely generated m-rigid groups. Also, it is proved that the theory 𝔗 m admits quantifier elimination down to a Boolean combination of ∀∃-formulas.
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