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The class of groups which have a subgroup of index 2 is not elementary

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Abstract.

F. Oger proved that if A is a finite group, then the class of groups which are abelian-by-A can be axiomatized by a single first order sentence. It is established here that, in Oger's result, the word abelian cannot be replaced by group.

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Authors and Affiliations

  1. Équipe de Logique Mathématique, Université Paris 7, UFR de Mathématiques, 2 place Jussieu, 75251 Paris Cedex 05, France. e-mail: coulbois@logique.jussieu.fr, , , , , , FR

    Thierry Coulbois

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  1. Thierry Coulbois
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Received: 15 March 1996 / Published online: 18 July 2001

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Coulbois, T. The class of groups which have a subgroup of index 2 is not elementary. Arch. Math. Logic 40, 523–524 (2001). https://doi.org/10.1007/s001530100085

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  • DOI: https://doi.org/10.1007/s001530100085

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