Finite one-generator skew braces correspond exactly to indecomposable solutions whose q-cycle set is generated by one element, with irreducible solutions matching braces generated by every element.
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One-generator skew braces and indecomposable set-theoretic solutions to the Yang-Baxter equation
Finite one-generator skew braces correspond exactly to indecomposable solutions whose q-cycle set is generated by one element, with irreducible solutions matching braces generated by every element.