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arXiv · 2606.28177

Chain conditions on skew braces and solutions of the Yang-Baxter Equation

Massimiliano Di Matteo·Ramón Esteban-Romero·Maria Ferrara·Vicent Pérez-Calabuig
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Abstract

Classical works of Hall and McLain show that solubility and local nilpotency play a key role in deriving finite generation in groups from maximal or minimal conditions on normal subgroups. In this work, brace-theoretical analogues of Hall's and McLain's results are analysed for skew braces satisfying the maximal or minimal condition on ideals. We also introduce finiteness and chain conditions on non-degenerate set-theoretic solutions of the Yang-Baxter equation, and their impact on associated structure and permutation skew braces of solutions is also described.

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Massimiliano Di Matteo, Ramón Esteban-Romero, Maria Ferrara, Vicent Pérez-Calabuig. 2026-07-13. Chain conditions on skew braces and solutions of the Yang-Baxter Equation. https://arxiv.org/abs/2606.28177

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