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PreprintCC BY 4.0arXiv

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

  • Paul J. Truman
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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. 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 $ pq $, where $ p,q $ are distinct prime numbers.

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Cite

BibTeXRIS
BibTeX
@misc{truman2026analogues,
  title = {{Analogues of Sylow's first theorem, Cauchy's theorem, and Hall's theorem for skew braces}},
  author = {Paul J. Truman},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2606.18414},
  eprint = {2606.18414},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.18414},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Analogues of Sylow's first theorem, Cauchy's theorem, and Hall's theorem for skew braces
AU  - Paul J. Truman
PY  - 2026
DA  - 2026/09/22
PB  - arXiv
DO  - 10.48550/arxiv.2606.18414
UR  - https://arxiv.org/abs/2606.18414
AB  - 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 $ pq $, where $ p,q $ are distinct prime numbers.
ER  -