Linearity of groups definable in o-minimal structures

DOI10.1007/s00029-016-0247-9zbMath1423.03132OpenAlexW2469696499MaRDI QIDQ522675

Frécon, Olivier

Publication date: 18 April 2017

Published in: Selecta Mathematica. New Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00029-016-0247-9

zbMATH Keywords

real closed fieldo-minimal structureLevi subgroup

Mathematics Subject Classification ID

General structure theorems for groups (20E34) Linear algebraic groups over the reals, the complexes, the quaternions (20G20) General properties and structure of real Lie groups (22E15) Model theory of ordered structures; o-minimality (03C64)

Related Items

Cartan subgroups and regular points of o‐minimal groups

Cites Work

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• On groups and fields definable in o-minimal structures
• Finite soluble groups
• Nilpotent groups
• Solvable groups definable in o-minimal structures.
• A signalizer functor theorem for groups of finite Morley rank.
• Definable homomorphisms of abelian groups in o-minimal structures
• On Levi subgroups and the Levi decomposition for groups definable in o-minimal structures
• Commutators in groups definable in o-minimal structures
• Interpretable groups are definable
• CONJUGACY OF CARTER SUBGROUPS IN GROUPS OF FINITE MORLEY RANK
• Groupes géométriques de rang de Morley fini
• On divisibility in definable groups
• Pseudo-tori and subtame groups of finite Morley rank
• A growth dichotomy for o-minimal expansions of ordered groups
• Definable Compactness and Definable Subgroups of o-Minimal Groups
• Definably simple groups in o-minimal structures
• Simple algebraic and semialgebraic groups over real closed fields
• On Groups and Rings Definable In O-Minimal Expansions of Real Closed Fields
• Around unipotence in groups of finite Morley rank
• Model completeness results for expansions of the ordered field of real numbers by restricted Pfaffian functions and the exponential function
• Good tori in groups of finite Morley rank
• Generalized Hall subgroups in soluble groups of finite Morley rank
• Linear groups definable in o-minimal structures