论文标题
有限偏括号，可解决的添加剂组
Finite skew braces with solvable additive group
论文作者
论文摘要
A. smoktunowicz和L. vendramin猜想，如果$ a $是有限的偏斜支撑，可解决的添加剂组，那么$ a $的乘法组是可解决的。在此简短的说法中，我们朝着积极解决这个猜想迈出了一步，证明如果$ a $是最小的有限偏斜支撑，可解决的添加剂组和不可溶解的乘法组，那么$ a $的乘法组并不简单。在获得此结果的路上，我们证明了A. smoktunowicz和L. vendramin的猜想在$ a $ $ 3 $不可分解的情况下是正确的。
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 $3$.
