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 languageEnglish
Pages (from-to)172-183
Number of pages12
JournalJournal of Algebra
Volume574
DOIs
Publication statusPublished - 15 May 2021

Keywords

  • Simple group
  • Skew brace
  • Solvable group

OECD FOS+WOS

  • 1.01 MATHEMATICS

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