Existentially closed CSA-groups
نویسندگان
چکیده
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 the same maximal abelian subgroups, except maybe the infinite cyclic ones. We deduce from this that there exist 20 countable existentially closed CSA-groups without involutions and that their firstorder theories have 20 types over ∅.
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