PreprintCC BY 4.0arXiv
On π-nilpotencies of finite skew braces
Abstract
Let π be a set of primes. We extend the theory of left and right π-nilpotency in skew braces beyond the nilpotent type setting, and introduce the study of central π-nilpotency for finite skew braces. We investigate the relationships between these three notions, and a characterisation of central π-nilpotency in terms of chief factors is also established. This leads to the introduction of the π-Fitting ideal of a skew brace, for which we prove a local analogue of Fitting's theorem and provide a description in terms of centralisers of chief factors. Finally, we introduce the π-core of a skew brace and investigate its relationship with π-ideals and central π-nilpotency.
Related
- Determinant characters and multiplicative solubility of finite skew braces
- Bisoluble and Binilpotent Skew Braces of Finite Morley Rank
- Classification of finite left-simple skew braces
- The Left-Nilpotent Residual and Its Supplements in Finite Skew Braces
- Relative commuting probability and BFC-type results for finite skew braces
BibTeX
@misc{gong2026πnilpotencies,
title = {{On $π$-nilpotencies of finite skew braces}},
author = {L. Gong and M. Damele and V. Pérez-Calabuig and A. Rodríguez-Durà},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.37042},
eprint = {2610.37042},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.37042},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On π-nilpotencies of finite skew braces
AU - L. Gong
AU - M. Damele
AU - V. Pérez-Calabuig
AU - A. Rodríguez-Durà
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.37042
UR - https://arxiv.org/abs/2610.37042
AB - Let π be a set of primes. We extend the theory of left and right π-nilpotency in skew braces beyond the nilpotent type setting, and introduce the study of central π-nilpotency for finite skew braces. We investigate the relationships between these three notions, and a characterisation of central π-nilpotency in terms of chief factors is also established. This leads to the introduction of the π-Fitting ideal of a skew brace, for which we prove a local analogue of Fitting's theorem and provide a description in terms of centralisers of chief factors. Finally, we introduce the π-core of a skew brace and investigate its relationship with π-ideals and central π-nilpotency.
ER -