A group G is said to be rigid if it contains a normal series G = G₁ > G₂ > … > G_m > G_m+1 = 1, whose quotients G_i/G_i+1 are Abelian and, when treated as right 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 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.

中文翻译：

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可分割的刚性组。IV。可定义的子组

如果组G包含一个正规序列G = G ₁ > G ₂ >…> G _m > G _{m +1} = 1，则它是刚性的，其商G _i / G _{i +1}是阿贝尔的，当被视为右ℤ[ G / G _i ]-模块，无扭转。如果商G _i / G _{i +1}的元素可以被环[[ G / G]的非零元素整除，则刚性群G是可整除的_我]。我们描述了可分割刚性组的子组，这些子组在无参数和有参数的组理论的签名中是可定义的。