PreprintCC0arXiv
Classification of finite left-simple skew braces
Abstract
We give a complete classification of finite left-simple skew braces. We prove that a non-trivial finite skew brace has no non-trivial proper left ideals if and only if it is either the trivial skew brace of prime order or the almost trivial skew brace associated with a finite non-abelian simple group.
Related
- Classification of skew left braces with additive group isomorphic to the infinite dihedral group
- The Left-Nilpotent Residual and Its Supplements in Finite Skew Braces
- Inverse Baer deformations and finite simple skew braces of nilpotent type
- Kernel--wreath constructions and infinite families of finite simple skew braces
- Skew braces whose left series is not generated by right-normed star products
BibTeX
@misc{damele2026classification,
title = {{Classification of finite left-simple skew braces}},
author = {Marco Damele},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.35542},
eprint = {2609.35542},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.35542},
note = {CC0},
}
RIS
TY - UNPB
TI - Classification of finite left-simple skew braces
AU - Marco Damele
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.35542
UR - https://arxiv.org/abs/2609.35542
AB - We give a complete classification of finite left-simple skew braces. We prove that a non-trivial finite skew brace has no non-trivial proper left ideals if and only if it is either the trivial skew brace of prime order or the almost trivial skew brace associated with a finite non-abelian simple group.
ER -