Universal theories for partially commutative metabelian groups.

DOI10.1007/S10469-011-9120-2zbMath1263.20032OpenAlexW2028255661MaRDI QIDQ694217

E. I. Timoshenko, Chander Kanta Gupta

Publication date: 11 December 2012

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

Full work available at URL: https://doi.org/10.1007/s10469-011-9120-2

zbMATH Keywords

centralizersannihilatorsfinitely presented groupsuniversal theorieselementary equivalencesuniversal equivalencespartially commutative metabelian groupsvarieties 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 (16)

Mal’tsev bases for partially commutative nilpotent groups ⋮ Comparison between the universal theories of partially commutative metabelian groups ⋮ On splittings, subgroups, and theories 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. ⋮ Elementary equivalence of partially commutative Lie rings and algebras ⋮ Universal equivalence of partially commutative metabelian Lie algebras ⋮ A basis for a partially commutative metabelian group ⋮ On embedding of partially commutative metabelian groups to matrix groups ⋮ Partially commutative groups and Lie algebras ⋮ Centralizer dimensions of partially commutative metabelian groups ⋮ On universal equivalence of partially commutative Lie algebras defined by graphs without triangles and squares and with no isolated vertices ⋮ 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

Cites Work

• Unnamed Item
• Partially commutative metabelian groups: centralizers and elementary equivalence.
• Universal equivalence of partially commutative metabelian groups.
• Structure of the automorphism group for partially commutative class two nilpotent groups.
• Orthogonal systems in finite graphs
• Commutators of Certain Finitely Generated Soluble Groups

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