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...
متن کاملOn Superstable Groups
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...
متن کاملA note on superstable groups
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...
متن کاملSuperstable 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...
متن کاملExistentially closed CSA-groups
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 tha...
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ژورنال
عنوان ژورنال: Annals of Pure and Applied Logic
سال: 2008
ISSN: 0168-0072
DOI: 10.1016/j.apal.2006.04.005