1. Finite skew braces with solvable additive group
- Author
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Gorshkov, Ilya and Nasybullov, Timur
- Subjects
Mathematics - Group Theory ,20F16, 20D05, 20N99, 16T25 - 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 $3$.
- Published
- 2020