English

A note on right-nil and strong-nil skew braces

Group Theory 2024-12-10 v3 Rings and Algebras

Abstract

The aim of this short note is to completely answer Questions 2.34 and 2.35 of arXiv:1806.01127. In particular, we show that a finite strong-nil skew brace BB of abelian type need not be right-nilpotent, but that this is the case if~BB is of nilpotent type and bb=0b\ast b=0 for all bBb\in B (our examples show that this is the best possible result).

Keywords

Cite

@article{arxiv.2310.11123,
  title  = {A note on right-nil and strong-nil skew braces},
  author = {Adolfo Ballester-Bolinches and Maria Ferrara and Vicent Pérez-Calabuig and Marco Trombetti},
  journal= {arXiv preprint arXiv:2310.11123},
  year   = {2024}
}

Comments

Accepted version to be published in Proc. Royal Soc. Edinburgh Section A

R2 v1 2026-06-28T12:53:07.876Z