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arXiv · 2006.00466

Finite skew braces with solvable additive group

Ilya Gorshkov·Timur Nasybullov
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Abstract

A. Smoktunowicz and L. Vendramin conjectured that if $A$ is a finite skew brace with solvable additive group, then the multiplicative group of $A$ is solvable. In this short note we make a step towards positive solution of this conjecture proving that if $A$ is a minimal finite skew brace with solvable additive group and non-solvable multiplicative group, then the multiplicative group of $A$ is not simple. On the way to obtaining this result, we prove that the conjecture of A. Smoktunowicz and L. Vendramin is correct in the case when the order of $A$ is not divisible by $3$.

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Ilya Gorshkov, Timur Nasybullov. 2020-05-31. Finite skew braces with solvable additive group. https://arxiv.org/abs/2006.00466

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