We prove conjugacy and generic disjointness of generous Carter subgroups in groups of finite Morley rank. We elaborate on groups with a generous Carter subgroup and on a minimal counterexample to the Gener-icity Conjecture.
We give two slight generalizations of results of Poizat about elementary theories of groups obtained by free constructions. The first-one concerns generic types and the non-superstability of such groups in many cases. The second-one concerns the connectedness of most free products of groups without amalgamation. First-order theories of free products of… (More)
Any countable Kn-free graph T embeds as a moiety into the universal homogeneous Kn-free graph Kn in such a way that every automorphism of T extends to a unique automorphism of Kn. Furthermore , there are 2 ω such embeddings which are pairwise not conjugate under Aut(Kn).
In continuation of [JOH04, OH07], we prove that existentially closed CSA-groups have the independence property. This is done by showing that there exist words having the independence property relative to the class of torsion-free hyperbolic groups.