Abelian‐by‐G Groups, for G Finite, from the Model Theoretic Point of View

Mathematical Logic Quarterly 40 (1):125-131 (1994)
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Let G be a finite group. We prove that the theory af abelian-by-G groups is decidable if and only if the theory of modules over the group ring ℤ[G] is decidable. Then we study some model theoretic questions about abelian-by-G groups, in particular we show that their class is elementary when the order of G is squarefree



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An undecidability theorem for lattices over group rings.Carlo Toffalori - 1997 - Annals of Pure and Applied Logic 88 (2-3):241-262.

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Model Theory and Modules.Mike Prest - 1989 - Journal of Symbolic Logic 54 (3):1115-1118.

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