The class of groups which have a subgroup of index 2 is not elementary |
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| Authors: | Thierry Coulbois |
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| Affiliation: | (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 |
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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. Received: 15 March 1996 / Published online: 18 July 2001 |
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| Keywords: | Mathematics Subject Classification (2000): 03C60 20A05 20F22 |
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