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arXiv · 2409.18410

On Gr\"{u}n's lemma for perfect skew braces

Cindy Tsang
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Abstract

By previous work of Ced\'{o}, Smoktunowicz, and Vendramin, one already knows that the analog of Gr\"{u}n's lemma fails to hold for perfect skew left braces when the socle is used as an analog of the center of a group. In this paper, we use the annihilator instead of the socle. We shall show that the analog of Gr\"{u}n's lemma holds for perfect two-sided skew braces but not in general.

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Cindy Tsang. 2024-09-27. On Gr\"{u}n's lemma for perfect skew braces. https://doi.org/10.2969/jmsj%2F94549454

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