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arXiv · 2208.03490

Left seminear-rings, groups semidirect products and left cancellative left semi-braces

Marco Castelli
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Abstract

We study some relations between left cancellative left semi-braces and other existing algebraic structures. In particular, we show that every left semi-brace arises from a left seminear-ring, extending the correspondence given by Rump between skew left braces and left near-rings in \cite{rump2019set}. Moreover, we show a correspondence between certain groups semidirect products and left cancellative left semi-braces satisfying an additional hypothesis on the set of idempotents. As an application, we classify left cancellative left semi-braces of size $pq$ and $2p^2$ such that the set of idempotents $E$ is a Sylow subgroup of the multiplicative group. Finally, we study various type of nilpotency, recently introduced in \cite{catino2022nilpotency}, of these left semi-braces.

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Marco Castelli. 2022-08-06. Left seminear-rings, groups semidirect products and left cancellative left semi-braces. https://arxiv.org/abs/2208.03490

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