Sylow and Hall theorems for finite skew braces are direct consequences of the Sylow and Hall structures of finite trifactorised groups.
Analogues of Sylow's first theorem, Cauchy's theorem, and Hall's theorem for skew braces
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abstract
We establish an unconditional analogue of Sylow's first theorem for finite skew braces, and deduce an analogue of Cauchy's theorem. We also prove an analogue of the existence part of Hall's theorem for finite skew braces with soluble additive and multiplicative groups.
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2026 1verdicts
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On finite trifactorised groups and Sylow and Hall theorems for skew braces
Sylow and Hall theorems for finite skew braces are direct consequences of the Sylow and Hall structures of finite trifactorised groups.