Commutator theory for loops.

DOI10.1016/J.JALGEBRA.2013.08.045zbMath1319.20056arXiv1509.05730OpenAlexW2962888838MaRDI QIDQ397857

Petr Vojtěchovský, David Stanovský

Publication date: 12 August 2014

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1509.05730

zbMATH Keywords

solvabilityassociatorsnilpotencycommutator theoryassociator subloopcentral nilpotencycommutators of normal subloopscongruence commutatorsderived subloopinner mappingstotal inner mapping groupsvarieties of loops

Mathematics Subject Classification ID

Loops, quasigroups (20N05) Subalgebras, congruence relations (08A30) Congruence modularity, congruence distributivity (08B10)

Related Items (17)

Prime radical of loops and \(\Omega\)-loops. I. ⋮ Middle Bruck loops and the total multiplication group ⋮ Medial and semimedial left quasigroups ⋮ The prime radical of alternative rings and loops ⋮ Central nilpotency of skew braces ⋮ Extensions and tangent prolongations of differentiable loops ⋮ On abelian-by-cyclic Moufang loops ⋮ DIVISION SUDOKUS: INVARIANTS, ENUMERATION, AND MULTIPLE PARTITIONS ⋮ Abelian congruences and solvability in Moufang loops ⋮ Three concepts of nilpotence in loops ⋮ Central reflections and nilpotency in exact Mal'tsev categories ⋮ Commutator theory for racks and quandles ⋮ Abelian extensions and solvable loops. ⋮ Topological loops having solvable indecomposable Lie groups as their multiplication groups ⋮ Generating subdirect products ⋮ Moufang Loops and Groups with Triality are Essentially the Same Thing ⋮ Basarab loop and the generators of its total multiplication group

Uses Software

• GAP
• Mace4
• LOOPS

Cites Work

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• The structure of finite algebras
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• Homomorphisms of Non-Associative Systems

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