Divisible rigid groups. Algebraic closedness and elementary theory

DOI10.1007/s10469-017-9461-6zbMath1403.20050OpenAlexW2771939450MaRDI QIDQ1703282

N. S. Romanovskii

Publication date: 2 March 2018

Published in: Algebra and Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10469-017-9461-6

zbMATH Keywords

elementary theorydivisible rigid groupalgebraic closedness

Mathematics Subject Classification ID

Model-theoretic algebra (03C60) Derived series, central series, and generalizations for groups (20F14) Limits, profinite groups (20E18) Algebraic geometry over groups; equations over groups (20F70)

Related Items

Generalized rigid groups: definitions, basic properties, and problems, Divisible rigid groups. Morley rank, Equational Noethericity of metabelian \(r\)-groups, Generic types and generic elements in divisible rigid groups, Divisible rigid groups. IV: Definable subgroups, Generalized rigid metabelian groups, Divisible rigid groups. III: Homogeneity and quantifier elimination, Divisible rigid groups. II: Stability, saturation, and elementary submodels, Two facts on model theory for divisible rigid groups

Cites Work

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• The Magnus embedding as a special case of a homological construction.
• Decomposition of a group over an abelian normal subgroup
• Applications of a New K-Theoretic Theorem to Soluble Group Rings
• The property of being equationally Noetherian for some soluble groups
• Model Theory
• A Note on Zero Divisors in Group-Rings