Properties and universal theories for partially commutative nilpotent metabelian groups.

DOI10.1007/s10469-012-9192-7zbMath1284.20030OpenAlexW2001905987MaRDI QIDQ1936282

E. I. Timoshenko, Chander Kanta Gupta

Publication date: 21 February 2013

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

Full work available at URL: https://doi.org/10.1007/s10469-012-9192-7

zbMATH Keywords

centralizerstreesannihilatorsgraphs of groupsuniversal theoriespartially commutative nilpotent groupspartially commutative metabelian groups

Mathematics Subject Classification ID

Solvable groups, supersolvable groups (20F16) Model-theoretic algebra (03C60) Generators, relations, and presentations of groups (20F05) Nilpotent groups (20F18) 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 (5)

On the decomposition of partially commutative groups of varieties and their defining graphs ⋮ Universal equivalence of some countably generated partially commutative structures ⋮ A basis for a partially commutative metabelian group ⋮ On embedding of partially commutative metabelian groups to matrix groups ⋮ Partially commutative groups and Lie algebras

Cites Work

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• Partially commutative metabelian groups: centralizers and elementary equivalence.
• Universal equivalence of partially commutative metabelian groups.
• Universal equivalence of partially commutative nilpotent groups.
• Universal theories for partially commutative metabelian groups.
• A Mal'tsev basis for a partially commutative nilpotent metabelian group.
• Generators for the automorphism groups of free metabelian pro-\(p\)-groups

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