Finite skew braces with solvable additive group

2020/05/31 by Gorshkov, Ilya, Nasybullov, Timur · 4 citations
#16T25 #20D05 #20F16 #20N99 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2006.00466

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.

Cited by

• A Counterexample to Byott's Conjecture for Finite Skew Braces
• Comparison of addition and multiplication in a skew brace
• Finite groups in which every proper characteristic subgroup is cyclic
• Structural and rigidity properties of Lie skew braces

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