scientific article; zbMATH DE number 1522509
From MaRDI portal
Publication:4510744
zbMath0961.03034MaRDI QIDQ4510744
Publication date: 28 May 2001
Title: zbMATH Open Web Interface contents unavailable due to conflicting licenses.
surveystabilitychain conditionsgeneric typesstable groupsdefinable groupsfinite Morley ranksuperstable groupsone-basedness
Applications of logic to group theory (20A15) Model-theoretic algebra (03C60) Classification theory, stability, and related concepts in model theory (03C45)
Related Items
Hyperbolically embedded subgroups and rotating families in groups acting on hyperbolic spaces ⋮ Some inevitable reflexions ⋮ Medium and symmetry, a study of convexity in groups without involutions ⋮ Interpretable groups in Mann pairs ⋮ Acylindrically hyperbolic groups
Cites Work
- Minimale Gruppen
- Группы и кольца, теория которых категорична
- Instabilité Des Corps Formellement Réels
- Bad groups of finite Morley rank
- Definability and definable groups in simple theories
- A note on Lascar strong types in simple theories
- Small fields
- Model theory of difference fields
- On central extensions of algebraic groups
- CM-triviality and stable groups
- Équations génériques dans un groupe stable nilpotent
- Lascar strong types in some simple theories
- Quasi-endomorphisms in small stable groups
- Le Canada Semi-Dry
- Conditions of quasi-nilpotency in certain varieties of groups
- Schur-Zassenhaus theorem revisited
- An Almost Strongly Minimal Non-Desarguesian Projective Plane
- A note on defining groups in stable structures
- Groups and Fields Interpretable in Separably Closed Fields
- On CN-Groups of Finite Morley Rank
- Definable Compactness and Definable Subgroups of o-Minimal Groups
- From Stability to Simplicity
- Largeur et nilpotence
- Definably simple groups in o-minimal structures
- Simple algebraic and semialgebraic groups over real closed fields
- Liftez les sylows! Une suite à “Sous-groupes périodiques d'un groupe stable”
- Supersimple ω-categorical groups and theories
- Supersimple theories
- Quasi-o-minimal structures
- Zariski geometries
- A Hall Theorem for ω-Stable Groups
- Forking in Simple Unstable Theories
- A new uncountably categorical group
- Corps et chirurgie
- On Groups and Rings Definable In O-Minimal Expansions of Real Closed Fields
- Zariski geometries
- The geometry of forking and groups of finite Morley rank
- Coordinatisation and canonical bases in simple theories
- Constructing ω-stable structures: rank 2 fields
- On Solvable Groups of Finite Morley Rank
- Categoricity in Power
- On $ω_1$-categorical theories of fields
- On $ω_1$-categorical theories of abelian groups
- The Mordell-Lang conjecture for function fields
- Model completeness results for expansions of the ordered field of real numbers by restricted Pfaffian functions and the exponential function
- On Algebraic Groups of Transformations
- Superstable fields and groups
- Groups of mixed type
- Groups of mixed type
- The Manin-Mumford conjecture and the model theory of difference fields
- Locally modular theories of finite rank
- A new strongly minimal set
- Commutator conditions and splitting automorphisms for stable groups
- Unidimensional theories are superstable
- Semisimple stable and superstable groups
- The Engel elements of a soluble group
- On sharply n-transitive superstable groups
- Almost orthogonal regular types
- \(\aleph _ 0\)-categorical, \(\aleph _ 0\)-stable structures
- Strongly minimal countably categorical theories. II
- Model theory of modules
- Strongly minimal countably categorical theories. III
- Superstable groups
- Superstable groups; a partial answer to conjectures of Cherlin and Zil'ber
- On groups and fields definable in o-minimal structures
- Solvable groups of finite Morley rank
- Groups with the minimal condition on centralizers
- Periodic locally soluble groups with the minimal condition on centralizers
- Strongly minimal countably categorical theories
- On type definable subgroups of a stable group
- More on \(\mathfrak R\)
- On generic structures
- Stable actions of torsion groups and stable soluble groups
- Differentially closed fields
- Elimination of quantifiers for modules
- Classification theory and the number of non-isomorphic models
- Totally categorical groups and rings
- On groups of finite Morley rank with weakly embedded subgroups
- Supersimple fields and division rings
- Nilpotency in groups with the minimal condition on centralizers
- Stable groups, mostly of finite exponent
- On stable torsion-free nilpotent groups
- Groups definable in local fields and pseudo-finite fields
- Nilpotent complements and Carter subgroups in stable \({\mathfrak R}\)
- The elementary theory of restricted analytic fields with exponentiation
- Pushing up and \(C(G,T)\) in groups of finite Morley rank of even type
- Some foundational questions concerning differential algebraic groups
- On the structure of stable groups
- Simple theories
- Model theory
- Abnormal subgroups in solvable groups of finite Morley rank
- Strongly minimal expansions of algebraically closed fields
- Non-solvable groups of Morley rank 3
- The Fitting subgroup of a stable group
- Universal theory of certain solvable groups and bounded Ore group rings
- Groups of finite Morley rank with strongly embedded subgroups
- Stable generic structures
- Toward classifying unstable theories
- Another stable group
- Definable homomorphisms of abelian groups in o-minimal structures
- A theorem of the complement and some new o-minimal structures
- Stable theories
- The elementary theory of finite fields
- Almost categorical theories
- HYPERDEFINABLE GROUPS IN SIMPLE THEORIES
- Groups definable in separably closed fields
- Groupes stables, avec types génériques réguliers
- Sous-groupes periodiques d'un groupe stable
- Tores et p-groupes
- Abelian groups with modular generic
- Subgroups of stable groups
- Some model theory of simple algebraic groups over algebraically closed fields
- Les Groupes ω-Stables de Rang Fini
- The geometry of weakly minimal types
- Pas d'imaginaires dans l'infini!
- Sur la théorie élémentaire des corps de fonctions
- Definable Sets in Ordered Structures. I
- On Superstable Groups
- Notes on the stability of separably closed fields
- Groups of small Morley rank
- Sous-groupes définissables d'un groupe stable
- Stability of nilpotent groups of class 2 and prime exponent
- Simple unstable theories
- Decidability and stability of free nilpotent lie algebras and free nilpotent p-groups of finite exponent
- Projective Planes in Algebraically Closed Fields
- Generalized Fitting subgroup of a group of finite Morley rank
- An infinite superstable group has infinitely many conjugacy classes
- Poly-separated and ω-stable nilpotent groups
- Small stable groups and generics
- Superstable differential fields
- À propos d'équations génériques
- On the Schur-Zassenhaus theorem for groups of finite Morley rank
- A remark on differential algebraic groups.
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item