Makanin-Razborov diagrams over free products.

zbMath1252.20043arXiv0902.2493MaRDI QIDQ716389

Zlil Sela, Eric Jaligot

Publication date: 28 April 2011

Published in: Illinois Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0902.2493

zbMATH Keywords

free productssystems of equationslimit groupsstable groupselementary equivalencesMakanin-Razborov diagramsfirst order theories

Mathematics Subject Classification ID

Model-theoretic algebra (03C60) Geometric group theory (20F65) Decidability of theories and sets of sentences (03B25) Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations (20E06) Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) (20F10) Hyperbolic groups and nonpositively curved groups (20F67) Classification theory, stability, and related concepts in model theory (03C45) Algebraic geometry over groups; equations over groups (20F70)

Related Items (8)

Discrete representations of finitely generated groups into PSL(2,R)${\rm PSL}(2,\mathbb {R})$ ⋮ Automorphisms of groups and a higher rank JSJ decomposition. I: RAAGs and a higher rank Makanin-Razborov diagram ⋮ On systems of equations over free products of groups. ⋮ Undecidability of equations in free Lie algebras ⋮ Two remarks on elementary theories of groups obtained by free constructions ⋮ On systems of equations over free partially commutative groups ⋮ Homomorphisms to acylindrically hyperbolic groups I: Equationally noetherian groups and families ⋮ Equations in acylindrically hyperbolic groups and verbal closedness

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