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arXiv · 2310.11123

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

Adolfo Ballester-Bolinches·Maria Ferrara·Vicent Pérez-Calabuig·Marco Trombetti
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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 $B$ of abelian type need not be right-nilpotent, but that this is the case if~$B$ is of nilpotent type and $b\ast b=0$ for all $b\in B$ (our examples show that this is the best possible result).

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Adolfo Ballester-Bolinches, Maria Ferrara, Vicent Pérez-Calabuig, Marco Trombetti. 2023-10-17. A note on right-nil and strong-nil skew braces. https://arxiv.org/abs/2310.11123

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