Partially commutative groups and Lie algebras

DOI10.33048/semi.2021.18.048OpenAlexW3199385783WikidataQ115222238 ScholiaQ115222238MaRDI QIDQ2033371

E. I. Timoshenko, Evgeniĭ Nikolaevich Poroshenko

Publication date: 17 June 2021

Published in: Sibirskie Èlektronnye Matematicheskie Izvestiya (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2011.10995

zbMATH Keywords

nilpotent groupLie algebracentralizermetabelian groupnilpotent Lie algebrabasisgrouppartially commutative groupuniversal theorypartially commutative Lie algebraelementary theorypro-p-groupgroup automorphismmetabelian Lie algebravarieties of Lie algebrascentralizer dimensiondecomposition of groupvarieties of group

Mathematics Subject Classification ID

Solvable groups, supersolvable groups (20F16) Nilpotent groups (20F18) Identities, free Lie (super)algebras (17B01) Automorphisms of infinite groups (20E36) Automorphism groups of groups (20F28) Quasivarieties and varieties of groups (20E10)

Related Items (1)

A basis for the commutator subgroup of a partially commutative metabelian pro-\(p\)-group

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Quasivarieties generated by partially commutative groups.
• Partially commutative metabelian groups: centralizers and elementary equivalence.
• Universal equivalence of partially commutative metabelian groups.
• Universal theories for partially commutative metabelian groups.
• On universal equivalence of partially commutative Lie algebras defined by graphs without triangles and squares and with no isolated vertices
• Graph algebras
• The free partially commutative Lie algebra: Bases and ranks
• 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
• Elementary equivalence of partially commutative Lie rings and algebras
• IA-automorphisms of metabelian products of two Abelian groups.
• Universal theory of certain solvable groups and bounded Ore group rings
• Properties and universal theories for partially commutative nilpotent metabelian groups.
• Centralizers in partially commutative Lie algebras
• Structure of the automorphism group for partially commutative class two nilpotent groups.
• Partially commutative metabelian pro-\(p\)-groups
• Elementary equivalence and direct product decompositions of partially commutative groups of varieties
• Automorphisms of partially commutative metabelian groups
• On a presentation of the automorphism group of a partially commutative metabelian group
• Universal equivalence of some countably generated partially commutative structures
• Free partially commutative structures
• Comparison between the universal theories of partially commutative metabelian groups
• Universal equivalence of partially commutative metabelian Lie algebras
• An introduction to right-angled Artin groups.
• CENTRALISER DIMENSION OF FREE PARTIALLY COMMUTATIVE NILPOTENT GROUPS OF CLASS 2
• Isomorphisms of Graph Groups
• ∀-free metabelian groups
• Discriminating groups and c-dimension
• A Generating Set for the Automorphism Group of a Graph Group
• On embedding of partially commutative metabelian groups to matrix groups
• On Universal Equivalence of Partially Commutative Metabelian Lie Algebras
• A faithful matrix representation for certain centre-y-metabelian groups

This page was built for publication: Partially commutative groups and Lie algebras