Superstable groups; a partial answer to conjectures of cherlin and zil'ber
نویسندگان
چکیده
منابع مشابه
On superstable CSA-groups
We prove that a non-abelian superstable CSA-group has an infinite definable simple subgroup all of whose proper definable subgroups are abelian. This imply in particular that the existence of non-abelian CSAgroup of finite Morley rank is equivalent to the existence of a simple bad group all whose definable proper subgroups are abelian. We give a new proof of a result of E. Mustafin and B. Poiza...
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It is proved that all groups of finite U -rank that have the descending chain condition on definable subgroups are totally transcendental. A corollary is that any stable group that is definable in an o-minimal structure is totally transcendental of finite Morley rank. Motivation for this paper is a problem concerning stable groups definable in ominimal structures. One theorem is that any defina...
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S. Shelah [20] has given a description of all countable complete theories T that permit a classification of their models. A necessary condition for T is superstability. A stable (superstable) group is a group interpreted in some stable (superstable) structure. It is equivalent to say that the groups investigated have additional relations and functions such that the whole structure is stable (su...
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15 صفحه اولSuperstable groups acting on trees
We study superstable groups acting on trees. We prove that an action of an ω-stable group on a simplicial tree is trivial. This shows that an HNN-extension or a nontrivial free product with amalgamation is not ωstable. It is also shown that if G is a superstable group acting nontrivially on a Λ-tree, where Λ = Z or Λ = R, and if G is either α-connected and Λ = Z, or if the action is irreducible...
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ژورنال
عنوان ژورنال: Annals of Pure and Applied Logic
سال: 1986
ISSN: 0168-0072
DOI: 10.1016/0168-0072(86)90036-9