Bulletin of the London Mathematical Society· 2026Q1
Analogues of Sylow's first theorem, Cauchy's theorem and Hall's theorem for skew braces
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- Q1SCImago
- 2026year
Short summary
Analogues of Sylow's first, Cauchy's, and Hall's theorems have been established for finite skew braces, streamlining the classification of specific skew braces.
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Key points
- Established unconditional analogues of Sylow's first and Cauchy's theorems for finite skew braces.
- Proved an analogue of the existence part of Hall's theorem for skew braces with soluble additive and multiplicative groups.
- Streamlined the classification of skew braces of order pq (p, q distinct primes) by applying these new theorems.
- Made observations regarding the number of Sylow subskew braces in various cases.
AI-generated from the title and abstract; the full text is not read.
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.
The authors' abstract, as published at the source. Bulletin of the London Mathematical Society, 2026 · DOI ↗
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Field: Discrete Mathematics and Combinatorics
Discrete Mathematics and CombinatoricsMathematics