Finite skew braces with solvable additive group

Ilya Gorshkov, Timur Nasybullov

Research output: Contribution to journalArticlepeer-review

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.

Original language English 172-183 12 Journal of Algebra 574 https://doi.org/10.1016/j.jalgebra.2021.01.027 Published - 15 May 2021

Keywords

• Simple group
• Skew brace
• Solvable group

OECD FOS+WOS

• 1.01 MATHEMATICS