Theoretical analysis reveals that Sylow and Hall theorems for skew braces derive directly from trifactorised group structures, indicating a natural emergence of Cauchy's theorem.
The aim of this short note is to show that the Sylow theorem (respectively Hall theorem) for finite skew braces proved by Truman in [4] is a direct consequence of the Sylow structure (resp. Hall structure) of a finite trifactorised group. A Cauchy theorem for finite skew braces naturally emerges.
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Ballester-Bolinches et al. (2026) studied this question.
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