Universal theories for rigid soluble groups.

DOI10.1007/S10469-012-9164-YzbMath1263.20034OpenAlexW2029470452MaRDI QIDQ695805

N. S. Romanovskii, Alexei G. Myasnikov

Publication date: 17 December 2012

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

Full work available at URL: https://doi.org/10.1007/s10469-012-9164-y

zbMATH Keywords

decidabilitydecidable theoriesuniversal equivalences\(p\)-rigid groupsexistential axiomsrecursive systems of universal axiomsrigid solvable groupsuniversal theories of groups

Mathematics Subject Classification ID

Applications of logic to group theory (20A15) Solvable groups, supersolvable groups (20F16) Model-theoretic algebra (03C60) Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) (20F10) Quasivarieties and varieties of groups (20E10) Derived series, central series, and generalizations for groups (20F14) Equational classes, universal algebra in model theory (03C05) Algebraic geometry over groups; equations over groups (20F70)

Related Items (13)

Partially divisible completions of rigid metabelian pro-\(p\)-groups ⋮ Algebraic sets in a finitely generated 2-step solvable rigid pro-\(p\)-group. ⋮ Generic types and generic elements in divisible rigid groups ⋮ Algebraic geometry over algebraic structures. VI: Geometrical equivalence ⋮ Divisible rigid groups. Algebraic closedness and elementary theory ⋮ Characterization of finitely generated groups by types ⋮ 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 ⋮ Geometric view on homogeneous groups ⋮ Rigid metabelian pro-\(p\)-groups. ⋮ Automorphisms of divisible rigid groups. ⋮ Logical aspects of the theory of divisible rigid groups.

Cites Work

• Unnamed Item
• Unnamed Item
• Krull dimension of solvable groups.
• On the theories of free solvable groups
• Algebraic geometry over groups. I: Algebraic sets and ideal theory
• Algebraic geometry over groups. II: Logical foundations
• Universal theory of certain solvable groups and bounded Ore group rings
• Applications of a New K-Theoretic Theorem to Soluble Group Rings
• The property of being equationally Noetherian for some soluble groups
• ∀-free metabelian groups
• A Note on Zero Divisors in Group-Rings

This page was built for publication: Universal theories for rigid soluble groups.