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PreprintCC0arXiv

Determinant characters and multiplicative solubility of finite skew braces

  • Marco Damele
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Abstract

Let B be a finite skew brace. We prove that if the additive derived subgroup (B,+)' is nilpotent, then the multiplicative group (B,·) is soluble. In particular, this holds for finite skew braces with supersoluble or metabelian additive group.

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Cite

BibTeXRIS
BibTeX
@misc{damele2026determinant,
  title = {{Determinant characters and multiplicative solubility of finite skew braces}},
  author = {Marco Damele},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.28420},
  eprint = {2610.28420},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.28420},
  note = {CC0},
}
RIS
TY  - UNPB
TI  - Determinant characters and multiplicative solubility of finite skew braces
AU  - Marco Damele
PY  - 2026
DA  - 2026/10/20
PB  - arXiv
DO  - 10.48550/arxiv.2610.28420
UR  - https://arxiv.org/abs/2610.28420
AB  - Let B be a finite skew brace. We prove that if the additive derived subgroup (B,+)' is nilpotent, then the multiplicative group (B,·) is soluble. In particular, this holds for finite skew braces with supersoluble or metabelian additive group.
ER  -