On $ω_1$-categorical theories of abelian groups

Angus Macintyre

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On some model theoretic problems concerning certain extensions of abelian groups by groups of finite exponent

Carlo Toffalori (2000)

Rendiconti del Seminario Matematico della Università di Padova

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Undecidable theories of valuated abelian groups

Peter H. Schmitt (1984)

Mémoires de la Société Mathématique de France

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An elementary class extending abelian-by- $G$ groups, for $G$ infinite

Carlo Toffalori (1996)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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We show that for no infinite group $G$ the class of abelian-by- $G$ groups is elementary, but, at least when $G$ is an infinite elementary abelian $p$ -group (with $p$ prime), the class of groups admitting a normal abelian subgroup whose quotient group is elementarily equivalent to $G$ is elementary.