Аннотация
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.
Язык оригинала | английский |
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Страницы (с-по) | 172-183 |
Число страниц | 12 |
Журнал | Journal of Algebra |
Том | 574 |
DOI | |
Состояние | Опубликовано - 15 мая 2021 |