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Study classifies finite left-simple skew braces, indicating their unique properties.
A skew brace A = (A,·,∘) is said to be left-simple if A≠1 and it has no left ideal other than $1$ and A. The purpose of this paper is to give a partial classification of the finite left-simple skew braces. A result of Stefanello and Trappeniers implies that finite left-simple skew braces correspond precisely to minimal Hopf--Galois structures on finite Galois extensions of fields.
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Cindy (Sin Yi) Tsang (2026) studied this question.
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