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Existentially closed CSA-groups
Authors:Eric Jaligot  Abderezak Ould Houcine
Institution:Équipe de Logique Mathématique, Université de Paris VII, 75251 Paris, France
Abstract:We study existentially closed CSA-groups. We prove that existentially closed CSA-groups without involutions are simple and divisible, and that their maximal abelian subgroups are conjugate. We also prove that every countable CSA-group without involutions embeds into a finitely generated one having, up to conjugacy, the same maximal abelian subgroups, except maybe the infinite cyclic ones. We deduce from this that there exist 2aleph, Hebrew0 countable existentially closed CSA-groups without involutions and that their first-order theories have 2aleph, Hebrew0 types over empty set.
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