Partially commutative metabelian groups: centralizers and elementary equivalence.

DOI10.1007/s10469-009-9051-3zbMath1245.20032OpenAlexW2061873078MaRDI QIDQ431687

E. I. Timoshenko, Chander Kanta Gupta

Publication date: 29 June 2012

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

Full work available at URL: https://doi.org/10.1007/s10469-009-9051-3

zbMATH Keywords

centralizerstreesannihilatorsfinitely presented groupselementary equivalencesuniversal equivalencesvariety of metabelian groups

Mathematics Subject Classification ID

Solvable groups, supersolvable groups (20F16) Model-theoretic algebra (03C60) Generators, relations, and presentations of groups (20F05) Classical first-order logic (03B10) Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) (20F10) Quasivarieties and varieties of groups (20E10) Algebraic geometry over groups; equations over groups (20F70)

Related Items (31)

Universal equivalence of some countably generated partially commutative structures ⋮ Mal’tsev bases for partially commutative nilpotent groups ⋮ Comparison between the universal theories of partially commutative metabelian groups ⋮ Quasivarieties generated by partially commutative groups. ⋮ On splittings, subgroups, and theories of partially commutative metabelian groups ⋮ Algebraic geometry over algebraic structures. II: Foundations ⋮ Universal equivalence of partially commutative metabelian groups. ⋮ Universal equivalence of partially commutative Lie algebras ⋮ Centralizer dimensions and universal theories for partially commutative metabelian groups ⋮ Properties and universal theories for partially commutative nilpotent metabelian groups. ⋮ Centralizers in partially commutative Lie algebras ⋮ Elementary equivalence and direct product decompositions of partially commutative groups of varieties ⋮ Two remarks on the first-order theories of Baumslag-Solitar groups ⋮ Intersection of centralizers in a partially commutative metabelian group ⋮ Elementary equivalence of partially commutative Lie rings and algebras ⋮ Universal equivalence of partially commutative metabelian Lie algebras ⋮ Automorphisms of partially commutative metabelian groups ⋮ A basis for a partially commutative metabelian group ⋮ Universal theories for partially commutative metabelian groups. ⋮ Bases for partially commutative Lie algebras ⋮ Partially commutative metabelian pro-\(p\)-groups ⋮ On embedding of partially commutative metabelian groups to matrix groups ⋮ Partially commutative groups and Lie algebras ⋮ Centralizer dimensions of partially commutative metabelian groups ⋮ Universal theories and centralizer dimensions of groups ⋮ Groups universally equivalent to the solvable Baumslag-Soliter group ⋮ On universal equivalence of partially commutative Lie algebras defined by graphs without triangles and squares and with no isolated vertices ⋮ On Universal Equivalence of Partially Commutative Metabelian Lie Algebras ⋮ On partially commutative groups and the relevant algebras with commutation ⋮ Group signature formulas constructed from graphs ⋮ On a presentation of the automorphism group of a partially commutative metabelian group

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