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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(More)
We consider groups G interpretable in a supersimple finite rank theory T such that T eq eliminates ∃ ∞. It is shown that G has a definable soluble radical. If G has rank 2, then if G is pseudofinite it is soluble-by-finite, and partial results are obtained under weaker hypotheses, such as unimodularity of the theory. A classification is obtained when T is(More)
In a connected group of finite Morley rank in which, generically, elements belong to connected nilpotent subgroups, proper normalizing cosets of definable subgroups are not generous. We explain why this is true and what consequences this has on an abstract theory of Weyl groups in groups of finite Morley rank. The only known infinite simple groups of finite(More)
In a connected group of finite Morley rank in which the generic element belongs to a connected nilpotent subgroup, proper normalizing cosets of definable subgroups are not generous. We explain why this is true and what consequences this has on an abstract theory of Weyl groups in groups of finite Morley rank. The only known infinite simple groups of finite(More)