Analogues of Sylow's first theorem, Cauchy's theorem and Hall's theorem for skew braces

Source abstract

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. We make some observations regarding the number of Sylow subskew braces of a skew brace in various cases. By applying these results, we streamline the classification of skew braces of order , where are distinct prime numbers.