Displaying similar documents to “The theory of abelian p-groups with the quantifier I is decidable”

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.