Equational Noethericity of metabelian \(r\)-groups

DOI10.1134/S0037446620010139zbMath1471.20027OpenAlexW3006925035MaRDI QIDQ2191348

N. S. Romanovskii

Publication date: 24 June 2020

Published in: Siberian Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0037446620010139

zbMATH Keywords

metabelian groupsolvable grouprigid groupequationally Noetherian group\(r\)-group

Mathematics Subject Classification ID

Solvable groups, supersolvable groups (20F16) Other classes of groups defined by subgroup chains (20F22) Derived series, central series, and generalizations for groups (20F14) Algebraic geometry over groups; equations over groups (20F70)

Related Items (3)

On the universal theories of generalized rigid metabelian groups ⋮ Coordinate groups of irreducible algebraic sets over divisible metabelian \(r\)-groups ⋮ Groups universally equivalent to the solvable Baumslag-Soliter group

Cites Work

• Divisible rigid groups.
• Equational Noetherianness of rigid soluble groups.
• Irreducible algebraic sets over divisible decomposed rigid groups.
• Krull dimension of solvable groups.
• Two theorems about equationally Noetherian groups
• Generalized rigid groups: definitions, basic properties, and problems
• Divisible rigid groups. Algebraic closedness and elementary theory
• Divisible rigid groups. II: Stability, saturation, and elementary submodels
• Generalized rigid metabelian groups
• Divisible rigid groups. III: Homogeneity and quantifier elimination
• Hilbert's Nullstellensatz in algebraic geometry over rigid soluble groups

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