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  1.  12
    Axiomatization of Abelian-by- G Groups for a Finite Group G.Francis Oger - 2001 - Archive for Mathematical Logic 40 (7):515-521.
    We show that, for each finite group G, there exists an axiomatization of the class of abelian-by-G groups with a single sentence. In the proof, we use the definability of the subgroups M n in an abelian-by-finite group M, and the Auslander-Reiten sequences for modules over an Artin algebra.
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  2.  5
    Elementary Equivalence of Rings with Finitely Generated Additive Groups.Alexei G. Myasnikov, Francis Oger & Mahmood Sohrabi - 2018 - Annals of Pure and Applied Logic 169 (6):514-522.
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  3.  15
    Elementary Equivalence for Abelian-by-Finite and Nilpotent Groups.Francis Oger - 2001 - Journal of Symbolic Logic 66 (3):1471-1480.
    We show that two abelian-by-finite groups are elementarily equivalent if and only if they satisfy the same sentences with two alternations of quantifiers. We also prove that abelian-by-finite groups satisfy a quantifier elimination property. On the other hand, for each integer n, we give some examples of nilpotent groups which satisfy the same sentences with n alternations of quantifiers and do not satisfy the same sentences with n + 1 alternations of quantifiers.
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  4.  24
    The Model Theory of Finitely Generated Finite-by-Abelian Groups.Francis Oger - 1984 - Journal of Symbolic Logic 49 (4):1115-1124.
    In [01], we gave algebraic characterizations of elementary equivalence for finitely generated finite-by-abelian groups, i.e. finitely generated FC-groups. We also provided several examples of finitely generated finite-by-abelian groups which are elementarily equivalent without being isomorphic. In this paper, we shall use our previous results to describe precisely the models of the theories of finitely generated finite-by-abelian groups and the elementary embeddings between these models.
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