Triply factorised groups and the structure of skew left braces

DOI10.1007/s40304-021-00239-6zbMath1490.81094OpenAlexW3201305373MaRDI QIDQ2141745

Adolfo Ballester-Bolinches, Ramón Esteban-Romero

Publication date: 25 May 2022

Published in: Communications in Mathematics and Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40304-021-00239-6

zbMATH Keywords

idealskew left bracefactorised skew left braceleft fitting idealleft nilpotent skew left braceright nilpotent skew left bracetrifactorised grouptriply factorised group

Mathematics Subject Classification ID

Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Finite nilpotent groups, (p)-groups (20D15) Products of subgroups of abstract finite groups (20D40) Yang-Baxter equations (16T25)

Related Items

Some group-theoretical approaches to skew left braces ⋮ Semi-affine structures on groups and semi-braces ⋮ Finite skew braces of square-free order and supersolubility ⋮ Schur covers of skew braces ⋮ Enumeration of left braces with additive group 𝐶₄×𝐶₄×𝐶₄

Uses Software

• GAP
• YangBaxter

Cites Work

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• On the \(\pi\)-nilpotent length of \(\pi\)-solvable groups
• Skew braces and the Yang–Baxter equation
• Computing skew left braces of small orders
• On some unsolved problems in quantum group theory
• Left Braces and the Quantum Yang–Baxter Equation
• Skew left braces of nilpotent type
• Retractability of solutions to the Yang–Baxter equation and p-nilpotency of skew braces
• Some Exact Results for the Many-Body Problem in one Dimension with Repulsive Delta-Function Interaction
• Endliche Gruppen I