论文标题
可解决的置换组的$ 3美元可解决
The $3$-closure of a solvable permutation group is solvable
论文作者
论文摘要
令$ m $为正整数，让$ω$成为有限的集合。 $ g \ leq \ operatorname {sym}（ω）$的$ m $ clubersus $是$ω$上最大的排列组，其轨道与$ g $相同的轨道诱导措施$ω^m $。 $ 1美元的额外限额和2美元的可解决排列组的门额不可解决。我们证明，可解决的置换组的$ m $ clubersy始终可以解决$ m \ geq3 $。
Let $m$ be a positive integer and let $Ω$ be a finite set. The $m$-closure of $G\leq\operatorname{Sym}(Ω)$ is the largest permutation group on $Ω$ having the same orbits as $G$ in its induced action on the Cartesian product $Ω^m$. The $1$-closure and $2$-closure of a solvable permutation group need not be solvable. We prove that the $m$-closure of a solvable permutation group is always solvable for $m\geq3$.
